(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 52406, 1605]*) (*NotebookOutlinePosition[ 53044, 1628]*) (* CellTagsIndexPosition[ 53000, 1624]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["(s-t)^2 Log[r+Sqrt[r^2+(s-t)^2]] +r Sqrt[r^2+(s-t)^2]", "Input"], Cell[OutputFormData["\<\ Log[r + Sqrt[r^2 + (s - t)^2]]*(s - t)^2 + r*Sqrt[r^2 + (s - t)^2]\ \>", "\<\ 2 2 2 2 2 Log[r + Sqrt[r + (s - t) ]] (s - t) + r Sqrt[r + (s - t) ]\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["c1=D[%,s]", "Input"], Cell[OutputFormData[ "\<\ (s - t)^3/((r + Sqrt[r^2 + (s - t)^2])*Sqrt[r^2 + (s - t)^2]) + 2*Log[r + Sqrt[r^2 + (s - t)^2]]*(s - t) + (r*(s - t))/Sqrt[r^2 + (s - t)^2]\ \>", "\<\ 3 (s - t) --------------------------------------------- + 2 2 2 2 (r + Sqrt[r + (s - t) ]) Sqrt[r + (s - t) ] 2 2 r (s - t) 2 Log[r + Sqrt[r + (s - t) ]] (s - t) + ------------------- 2 2 Sqrt[r + (s - t) ]\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["FortranForm[%]", "Input"], Cell["\<\ (r*(s - t))/Sqrt(r**2 + (s - t)**2) + - (s - t)**3/ - ((r + Sqrt(r**2 + (s - t)**2))*Sqrt(r**2 + (s - t)**2)) - + 2*(s - t)*Log(r + Sqrt(r**2 + (s - t)**2))\ \>", "Output"] }, Open ]], Cell[CellGroupData[{ Cell["D[Out[2],{s,2}]", "Input"], Cell[OutputFormData["\<\ -((s - t)^4/((r + Sqrt[r^2 + (s - t)^2])^2* (r^2 + (s - t)^2))) - (s - t)^4/((r + Sqrt[r^2 + (s - t)^2])* (r^2 + (s - t)^2)^(3/2)) + (5*(s - t)^2)/ ((r + Sqrt[r^2 + (s - t)^2])*Sqrt[r^2 + (s - t)^2]) - (r*(s - t)^2)/(r^2 + (s - t)^2)^(3/2) + 2*Log[r + Sqrt[r^2 + (s - t)^2]] + r/Sqrt[r^2 + (s - t)^2]\ \>", "\<\ 4 (s - t) -(------------------------------------------) - 2 2 2 2 2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 4 (s - t) -------------------------------------------- + 2 2 2 2 3/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 2 5 (s - t) --------------------------------------------- - 2 2 2 2 (r + Sqrt[r + (s - t) ]) Sqrt[r + (s - t) ] 2 r (s - t) 2 2 ------------------ + 2 Log[r + Sqrt[r + (s - t) ]] + 2 2 3/2 (r + (s - t) ) r ------------------- 2 2 Sqrt[r + (s - t) ]\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["FortranForm[%]", "Input"], Cell["\<\ r/Sqrt(r**2 + (s - t)**2) - - (r*(s - t)**2)/(r**2 + (s - t)**2)**1.5 + - (5*(s - t)**2)/ - ((r + Sqrt(r**2 + (s - t)**2))*Sqrt(r**2 + (s - t)**2)) - - (s - t)**4/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**1.5) - - (s - t)**4/ - ((r + Sqrt(r**2 + (s - t)**2))**2*(r**2 + (s - t)**2))\\ - + 2*Log(r + Sqrt(r**2 + (s - t)**2))\ \>", "Output"] }, Open ]], Cell[CellGroupData[{ Cell["D[Out[2],{s,3}]", "Input"], Cell[OutputFormData["\<\ (2*(s - t)^5)/ ((r + Sqrt[r^2 + (s - t)^2])^3*(r^2 + (s - t)^2)^(3/2)) + (3*(s - t)^5)/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)^2) + (3*(s - t)^5)/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(5/2)) - (9*(s - t)^3)/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)) - (9*(s - t)^3)/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(3/2)) + (3*r*(s - t)^3)/(r^2 + (s - t)^2)^(5/2) + (12*(s - t))/ ((r + Sqrt[r^2 + (s - t)^2])*Sqrt[r^2 + (s - t)^2]) - (3*r*(s - t))/(r^2 + (s - t)^2)^(3/2)\ \>", "\<\ 5 2 (s - t) --------------------------------------------- + 2 2 3 2 2 3/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 5 3 (s - t) ------------------------------------------- + 2 2 2 2 2 2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 5 3 (s - t) -------------------------------------------- - 2 2 2 2 5/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 3 9 (s - t) ------------------------------------------ - 2 2 2 2 2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 3 9 (s - t) -------------------------------------------- + 2 2 2 2 3/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 3 3 r (s - t) ------------------ + 2 2 5/2 (r + (s - t) ) 12 (s - t) --------------------------------------------- - 2 2 2 2 (r + Sqrt[r + (s - t) ]) Sqrt[r + (s - t) ] 3 r (s - t) ------------------ 2 2 3/2 (r + (s - t) )\ \>"], "Output"] }, Open ]], Cell[OutputFormData["\<\ Out()\ \>", "\<\ Out()\ \>"], "Input"], Cell[OutputFormData["\<\ Out()\ \>", "\<\ Out()\ \>"], "Input"], Cell[CellGroupData[{ Cell["FortranForm[Out[9]]", "Input"], Cell["\<\ (-3*r*(s - t))/(r**2 + (s - t)**2)**1.5 + - (12*(s - t))/ - ((r + Sqrt(r**2 + (s - t)**2))*Sqrt(r**2 + (s - t)**2)) - + (3*r*(s - t)**3)/(r**2 + (s - t)**2)**2.5 - - (9*(s - t)**3)/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**1.5) - - (9*(s - t)**3)/ - ((r + Sqrt(r**2 + (s - t)**2))**2*(r**2 + (s - t)**2))\\ - + (3*(s - t)**5)/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**2.5) + - (3*(s - t)**5)/ - ((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)**2) + - (2*(s - t)**5)/ - ((r + Sqrt(r**2 + (s - t)**2))**3* - (r**2 + (s - t)**2)**1.5)\ \>", "Output"] }, Open ]], Cell[CellGroupData[{ Cell["D[Out[2],{s,4}]", "Input"], Cell[OutputFormData["\<\ -((6*(s - t)^6)/ ((r + Sqrt[r^2 + (s - t)^2])^4*(r^2 + (s - t)^2)^2)) - (12*(s - t)^6)/ ((r + Sqrt[r^2 + (s - t)^2])^3*(r^2 + (s - t)^2)^(5/2)) - (15*(s - t)^6)/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)^3) - (15*(s - t)^6)/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(7/2)) + (28*(s - t)^4)/ ((r + Sqrt[r^2 + (s - t)^2])^3*(r^2 + (s - t)^2)^(3/2)) + (42*(s - t)^4)/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)^2) + (42*(s - t)^4)/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(5/2)) - (15*r*(s - t)^4)/(r^2 + (s - t)^2)^(7/2) - (39*(s - t)^2)/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)) - (39*(s - t)^2)/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(3/2)) + (18*r*(s - t)^2)/(r^2 + (s - t)^2)^(5/2) + 12/((r + Sqrt[r^2 + (s - t)^2])*Sqrt[r^2 + (s - t)^2]) - (3*r)/(r^2 + (s - t)^2)^(3/2)\ \>", "\<\ 6 6 (s - t) -(-------------------------------------------) - 2 2 4 2 2 2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 6 12 (s - t) --------------------------------------------- - 2 2 3 2 2 5/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 6 15 (s - t) ------------------------------------------- - 2 2 2 2 2 3 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 6 15 (s - t) -------------------------------------------- + 2 2 2 2 7/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 4 28 (s - t) --------------------------------------------- + 2 2 3 2 2 3/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 4 42 (s - t) ------------------------------------------- + 2 2 2 2 2 2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 4 42 (s - t) -------------------------------------------- - 2 2 2 2 5/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 4 15 r (s - t) ------------------ - 2 2 7/2 (r + (s - t) ) 2 39 (s - t) ------------------------------------------ - 2 2 2 2 2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 2 39 (s - t) -------------------------------------------- + 2 2 2 2 3/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 2 18 r (s - t) ------------------ + 2 2 5/2 (r + (s - t) ) 12 --------------------------------------------- - 2 2 2 2 (r + Sqrt[r + (s - t) ]) Sqrt[r + (s - t) ] 3 r ------------------ 2 2 3/2 (r + (s - t) )\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["FortranForm[%]", "Input"], Cell["\<\ (-3*r)/(r**2 + (s - t)**2)**1.5 + - 12/((r + Sqrt(r**2 + (s - t)**2))* - Sqrt(r**2 + (s - t)**2)) + - (18*r*(s - t)**2)/(r**2 + (s - t)**2)**2.5 - - (39*(s - t)**2)/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**1.5) - - (39*(s - t)**2)/ - ((r + Sqrt(r**2 + (s - t)**2))**2*(r**2 + (s - t)**2))\\ - - (15*r*(s - t)**4)/(r**2 + (s - t)**2)**3.5 + - (42*(s - t)**4)/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**2.5) + - (42*(s - t)**4)/ - ((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)**2) + - (28*(s - t)**4)/ - ((r + Sqrt(r**2 + (s - t)**2))**3* - (r**2 + (s - t)**2)**1.5) - - (15*(s - t)**6)/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**3.5) - - (15*(s - t)**6)/ - ((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)**3) - - (12*(s - t)**6)/ - ((r + Sqrt(r**2 + (s - t)**2))**3* - (r**2 + (s - t)**2)**2.5) - - (6*(s - t)**6)/ - ((r + Sqrt(r**2 + (s - t)**2))**4* - (r**2 + (s - t)**2)**2)\ \>", "Output"] }, Open ]], Cell[CellGroupData[{ Cell["D[Out[2],{s,5}]", "Input"], Cell[OutputFormData["\<\ (24*(s - t)^7)/ ((r + Sqrt[r^2 + (s - t)^2])^5*(r^2 + (s - t)^2)^(5/2)) + (60*(s - t)^7)/ ((r + Sqrt[r^2 + (s - t)^2])^4*(r^2 + (s - t)^2)^3) + (90*(s - t)^7)/ ((r + Sqrt[r^2 + (s - t)^2])^3*(r^2 + (s - t)^2)^(7/2)) + (105*(s - t)^7)/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)^4) + (105*(s - t)^7)/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(9/2)) - (120*(s - t)^5)/ ((r + Sqrt[r^2 + (s - t)^2])^4*(r^2 + (s - t)^2)^2) - (240*(s - t)^5)/ ((r + Sqrt[r^2 + (s - t)^2])^3*(r^2 + (s - t)^2)^(5/2)) - (300*(s - t)^5)/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)^3) - (300*(s - t)^5)/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(7/2)) + (105*r*(s - t)^5)/(r^2 + (s - t)^2)^(9/2) + (190*(s - t)^3)/ ((r + Sqrt[r^2 + (s - t)^2])^3*(r^2 + (s - t)^2)^(3/2)) + (285*(s - t)^3)/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)^2) + (285*(s - t)^3)/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(5/2)) - (150*r*(s - t)^3)/(r^2 + (s - t)^2)^(7/2) - (90*(s - t))/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)) - (90*(s - t))/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(3/2)) + (45*r*(s - t))/(r^2 + (s - t)^2)^(5/2)\ \>", "\<\ 7 24 (s - t) --------------------------------------------- + 2 2 5 2 2 5/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 7 60 (s - t) ------------------------------------------- + 2 2 4 2 2 3 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 7 90 (s - t) --------------------------------------------- + 2 2 3 2 2 7/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 7 105 (s - t) ------------------------------------------- + 2 2 2 2 2 4 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 7 105 (s - t) -------------------------------------------- - 2 2 2 2 9/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 5 120 (s - t) ------------------------------------------- - 2 2 4 2 2 2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 5 240 (s - t) --------------------------------------------- - 2 2 3 2 2 5/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 5 300 (s - t) ------------------------------------------- - 2 2 2 2 2 3 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 5 300 (s - t) -------------------------------------------- + 2 2 2 2 7/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 5 105 r (s - t) ------------------ + 2 2 9/2 (r + (s - t) ) 3 190 (s - t) --------------------------------------------- + 2 2 3 2 2 3/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 3 285 (s - t) ------------------------------------------- + 2 2 2 2 2 2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 3 285 (s - t) -------------------------------------------- - 2 2 2 2 5/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 3 150 r (s - t) ------------------ - 2 2 7/2 (r + (s - t) ) 90 (s - t) ------------------------------------------ - 2 2 2 2 2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 90 (s - t) -------------------------------------------- + 2 2 2 2 3/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 45 r (s - t) ------------------ 2 2 5/2 (r + (s - t) )\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["FortranForm[%]", "Input"], Cell["\<\ (45*r*(s - t))/(r**2 + (s - t)**2)**2.5 - - (90*(s - t))/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**1.5) - - (90*(s - t))/ - ((r + Sqrt(r**2 + (s - t)**2))**2*(r**2 + (s - t)**2))\\ - - (150*r*(s - t)**3)/(r**2 + (s - t)**2)**3.5 + - (285*(s - t)**3)/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**2.5) + - (285*(s - t)**3)/ - ((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)**2) + - (190*(s - t)**3)/ - ((r + Sqrt(r**2 + (s - t)**2))**3* - (r**2 + (s - t)**2)**1.5) + - (105*r*(s - t)**5)/(r**2 + (s - t)**2)**4.5 - - (300*(s - t)**5)/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**3.5) - - (300*(s - t)**5)/ - ((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)**3) - - (240*(s - t)**5)/ - ((r + Sqrt(r**2 + (s - t)**2))**3* - (r**2 + (s - t)**2)**2.5) - - (120*(s - t)**5)/ - ((r + Sqrt(r**2 + (s - t)**2))**4* - (r**2 + (s - t)**2)**2) + - (105*(s - t)**7)/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**4.5) + - (105*(s - t)**7)/ - ((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)**4) + - (90*(s - t)**7)/ - ((r + Sqrt(r**2 + (s - t)**2))**3* - (r**2 + (s - t)**2)**3.5) + - (60*(s - t)**7)/ - ((r + Sqrt(r**2 + (s - t)**2))**4* - (r**2 + (s - t)**2)**3) + - (24*(s - t)**7)/ - ((r + Sqrt(r**2 + (s - t)**2))**5* - (r**2 + (s - t)**2)**2.5)\ \>", "Output"] }, Open ]], Cell[CellGroupData[{ Cell["D[Out[2],{s,6}]", "Input"], Cell[OutputFormData["\<\ -((120*(s - t)^8)/ ((r + Sqrt[r^2 + (s - t)^2])^6*(r^2 + (s - t)^2)^3)) - (360*(s - t)^8)/ ((r + Sqrt[r^2 + (s - t)^2])^5*(r^2 + (s - t)^2)^(7/2)) - (630*(s - t)^8)/ ((r + Sqrt[r^2 + (s - t)^2])^4*(r^2 + (s - t)^2)^4) - (840*(s - t)^8)/ ((r + Sqrt[r^2 + (s - t)^2])^3*(r^2 + (s - t)^2)^(9/2)) - (945*(s - t)^8)/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)^5) - (945*(s - t)^8)/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(11/2)) + (648*(s - t)^6)/ ((r + Sqrt[r^2 + (s - t)^2])^5*(r^2 + (s - t)^2)^(5/2)) + (1620*(s - t)^6)/ ((r + Sqrt[r^2 + (s - t)^2])^4*(r^2 + (s - t)^2)^3) + (2430*(s - t)^6)/ ((r + Sqrt[r^2 + (s - t)^2])^3*(r^2 + (s - t)^2)^(7/2)) + (2835*(s - t)^6)/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)^4) + (2835*(s - t)^6)/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(9/2)) - (945*r*(s - t)^6)/(r^2 + (s - t)^2)^(11/2) - (1170*(s - t)^4)/ ((r + Sqrt[r^2 + (s - t)^2])^4*(r^2 + (s - t)^2)^2) - (2340*(s - t)^4)/ ((r + Sqrt[r^2 + (s - t)^2])^3*(r^2 + (s - t)^2)^(5/2)) - (2925*(s - t)^4)/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)^3) - (2925*(s - t)^4)/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(7/2)) + (1575*r*(s - t)^4)/(r^2 + (s - t)^2)^(9/2) + (750*(s - t)^2)/ ((r + Sqrt[r^2 + (s - t)^2])^3*(r^2 + (s - t)^2)^(3/2)) + (1125*(s - t)^2)/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)^2) + (1125*(s - t)^2)/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(5/2)) - (675*r*(s - t)^2)/(r^2 + (s - t)^2)^(7/2) - 90/((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)) - 90/((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(3/2)) + (45*r)/(r^2 + (s - t)^2)^(5/2)\ \>", "\<\ 8 120 (s - t) -(-------------------------------------------) - 2 2 6 2 2 3 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 8 360 (s - t) --------------------------------------------- - 2 2 5 2 2 7/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 8 630 (s - t) ------------------------------------------- - 2 2 4 2 2 4 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 8 840 (s - t) --------------------------------------------- - 2 2 3 2 2 9/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 8 945 (s - t) ------------------------------------------- - 2 2 2 2 2 5 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 8 945 (s - t) --------------------------------------------- + 2 2 2 2 11/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 6 648 (s - t) --------------------------------------------- + 2 2 5 2 2 5/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 6 1620 (s - t) ------------------------------------------- + 2 2 4 2 2 3 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 6 2430 (s - t) --------------------------------------------- + 2 2 3 2 2 7/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 6 2835 (s - t) ------------------------------------------- + 2 2 2 2 2 4 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 6 2835 (s - t) -------------------------------------------- - 2 2 2 2 9/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 6 945 r (s - t) ------------------- - 2 2 11/2 (r + (s - t) ) 4 1170 (s - t) ------------------------------------------- - 2 2 4 2 2 2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 4 2340 (s - t) --------------------------------------------- - 2 2 3 2 2 5/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 4 2925 (s - t) ------------------------------------------- - 2 2 2 2 2 3 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 4 2925 (s - t) -------------------------------------------- + 2 2 2 2 7/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 4 1575 r (s - t) ------------------ + 2 2 9/2 (r + (s - t) ) 2 750 (s - t) --------------------------------------------- + 2 2 3 2 2 3/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 2 1125 (s - t) ------------------------------------------- + 2 2 2 2 2 2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 2 1125 (s - t) -------------------------------------------- - 2 2 2 2 5/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 2 675 r (s - t) ------------------ - 2 2 7/2 (r + (s - t) ) 90 ------------------------------------------ - 2 2 2 2 2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 90 -------------------------------------------- + 2 2 2 2 3/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 45 r ------------------ 2 2 5/2 (r + (s - t) )\ \>"], "Output"] }, Open ]], Cell[OutputFormData["\<\ Out()\ \>", "\<\ Out()\ \>"], "Input"], Cell[CellGroupData[{ Cell["FortranForm[%]", "Input"], Cell["\<\ (45*r)/(r**2 + (s - t)**2)**2.5 - - 90/((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**1.5) - - 90/((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)) - - (675*r*(s - t)**2)/(r**2 + (s - t)**2)**3.5 + - (1125*(s - t)**2)/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**2.5) + - (1125*(s - t)**2)/ - ((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)**2) + - (750*(s - t)**2)/ - ((r + Sqrt(r**2 + (s - t)**2))**3* - (r**2 + (s - t)**2)**1.5) + - (1575*r*(s - t)**4)/(r**2 + (s - t)**2)**4.5 - - (2925*(s - t)**4)/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**3.5) - - (2925*(s - t)**4)/ - ((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)**3) - - (2340*(s - t)**4)/ - ((r + Sqrt(r**2 + (s - t)**2))**3* - (r**2 + (s - t)**2)**2.5) - - (1170*(s - t)**4)/ - ((r + Sqrt(r**2 + (s - t)**2))**4* - (r**2 + (s - t)**2)**2) - - (945*r*(s - t)**6)/(r**2 + (s - t)**2)**5.5 + - (2835*(s - t)**6)/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**4.5) + - (2835*(s - t)**6)/ - ((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)**4) + - (2430*(s - t)**6)/ - ((r + Sqrt(r**2 + (s - t)**2))**3* - (r**2 + (s - t)**2)**3.5) + - (1620*(s - t)**6)/ - ((r + Sqrt(r**2 + (s - t)**2))**4* - (r**2 + (s - t)**2)**3) + - (648*(s - t)**6)/ - ((r + Sqrt(r**2 + (s - t)**2))**5* - (r**2 + (s - t)**2)**2.5) - - (945*(s - t)**8)/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**5.5) - - (945*(s - t)**8)/ - ((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)**5) - - (840*(s - t)**8)/ - ((r + Sqrt(r**2 + (s - t)**2))**3* - (r**2 + (s - t)**2)**4.5) - - (630*(s - t)**8)/ - ((r + Sqrt(r**2 + (s - t)**2))**4* - (r**2 + (s - t)**2)**4) - - (360*(s - t)**8)/ - ((r + Sqrt(r**2 + (s - t)**2))**5* - (r**2 + (s - t)**2)**3.5) - - (120*(s - t)**8)/ - ((r + Sqrt(r**2 + (s - t)**2))**6* - (r**2 + (s - t)**2)**3)\ \>", "Output"] }, Open ]], Cell[CellGroupData[{ Cell["D[Out[2],{s,7}]", "Input"], Cell[OutputFormData["\<\ (720*(s - t)^9)/ ((r + Sqrt[r^2 + (s - t)^2])^7*(r^2 + (s - t)^2)^(7/2)) + (2520*(s - t)^9)/ ((r + Sqrt[r^2 + (s - t)^2])^6*(r^2 + (s - t)^2)^4) + (5040*(s - t)^9)/ ((r + Sqrt[r^2 + (s - t)^2])^5*(r^2 + (s - t)^2)^(9/2)) + (7560*(s - t)^9)/ ((r + Sqrt[r^2 + (s - t)^2])^4*(r^2 + (s - t)^2)^5) + (9450*(s - t)^9)/ ((r + Sqrt[r^2 + (s - t)^2])^3*(r^2 + (s - t)^2)^(11/2)) + (10395*(s - t)^9)/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)^6) + (10395*(s - t)^9)/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(13/2)) - (4200*(s - t)^7)/ ((r + Sqrt[r^2 + (s - t)^2])^6*(r^2 + (s - t)^2)^3) - (12600*(s - t)^7)/ ((r + Sqrt[r^2 + (s - t)^2])^5*(r^2 + (s - t)^2)^(7/2)) - (22050*(s - t)^7)/ ((r + Sqrt[r^2 + (s - t)^2])^4*(r^2 + (s - t)^2)^4) - (29400*(s - t)^7)/ ((r + Sqrt[r^2 + (s - t)^2])^3*(r^2 + (s - t)^2)^(9/2)) - (33075*(s - t)^7)/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)^5) - (33075*(s - t)^7)/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(11/2)) + (10395*r*(s - t)^7)/(r^2 + (s - t)^2)^(13/2) + (8568*(s - t)^5)/ ((r + Sqrt[r^2 + (s - t)^2])^5*(r^2 + (s - t)^2)^(5/2)) + (21420*(s - t)^5)/ ((r + Sqrt[r^2 + (s - t)^2])^4*(r^2 + (s - t)^2)^3) + (32130*(s - t)^5)/ ((r + Sqrt[r^2 + (s - t)^2])^3*(r^2 + (s - t)^2)^(7/2)) + (37485*(s - t)^5)/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)^4) + (37485*(s - t)^5)/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(9/2)) - (19845*r*(s - t)^5)/(r^2 + (s - t)^2)^(11/2) - (6930*(s - t)^3)/ ((r + Sqrt[r^2 + (s - t)^2])^4*(r^2 + (s - t)^2)^2) - (13860*(s - t)^3)/ ((r + Sqrt[r^2 + (s - t)^2])^3*(r^2 + (s - t)^2)^(5/2)) - (17325*(s - t)^3)/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)^3) - (17325*(s - t)^3)/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(7/2)) + (11025*r*(s - t)^3)/(r^2 + (s - t)^2)^(9/2) + (1680*(s - t))/ ((r + Sqrt[r^2 + (s - t)^2])^3*(r^2 + (s - t)^2)^(3/2)) + (2520*(s - t))/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)^2) + (2520*(s - t))/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(5/2)) - (1575*r*(s - t))/(r^2 + (s - t)^2)^(7/2)\ \>", "\<\ 9 720 (s - t) --------------------------------------------- + 2 2 7 2 2 7/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 9 2520 (s - t) ------------------------------------------- + 2 2 6 2 2 4 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 9 5040 (s - t) --------------------------------------------- + 2 2 5 2 2 9/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 9 7560 (s - t) ------------------------------------------- + 2 2 4 2 2 5 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 9 9450 (s - t) ---------------------------------------------- + 2 2 3 2 2 11/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 9 10395 (s - t) ------------------------------------------- + 2 2 2 2 2 6 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 9 10395 (s - t) --------------------------------------------- - 2 2 2 2 13/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 7 4200 (s - t) ------------------------------------------- - 2 2 6 2 2 3 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 7 12600 (s - t) --------------------------------------------- - 2 2 5 2 2 7/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 7 22050 (s - t) ------------------------------------------- - 2 2 4 2 2 4 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 7 29400 (s - t) --------------------------------------------- - 2 2 3 2 2 9/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 7 33075 (s - t) ------------------------------------------- - 2 2 2 2 2 5 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 7 33075 (s - t) --------------------------------------------- + 2 2 2 2 11/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 7 10395 r (s - t) ------------------- + 2 2 13/2 (r + (s - t) ) 5 8568 (s - t) --------------------------------------------- + 2 2 5 2 2 5/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 5 21420 (s - t) ------------------------------------------- + 2 2 4 2 2 3 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 5 32130 (s - t) --------------------------------------------- + 2 2 3 2 2 7/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 5 37485 (s - t) ------------------------------------------- + 2 2 2 2 2 4 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 5 37485 (s - t) -------------------------------------------- - 2 2 2 2 9/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 5 19845 r (s - t) ------------------- - 2 2 11/2 (r + (s - t) ) 3 6930 (s - t) ------------------------------------------- - 2 2 4 2 2 2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 3 13860 (s - t) --------------------------------------------- - 2 2 3 2 2 5/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 3 17325 (s - t) ------------------------------------------- - 2 2 2 2 2 3 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 3 17325 (s - t) -------------------------------------------- + 2 2 2 2 7/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 3 11025 r (s - t) ------------------ + 2 2 9/2 (r + (s - t) ) 1680 (s - t) --------------------------------------------- + 2 2 3 2 2 3/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 2520 (s - t) ------------------------------------------- + 2 2 2 2 2 2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 2520 (s - t) -------------------------------------------- - 2 2 2 2 5/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 1575 r (s - t) ------------------ 2 2 7/2 (r + (s - t) )\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["FortranForm[%]", "Input"], Cell["\<\ (-1575*r*(s - t))/(r**2 + (s - t)**2)**3.5 + - (2520*(s - t))/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**2.5) + - (2520*(s - t))/ - ((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)**2) + - (1680*(s - t))/ - ((r + Sqrt(r**2 + (s - t)**2))**3* - (r**2 + (s - t)**2)**1.5) + - (11025*r*(s - t)**3)/(r**2 + (s - t)**2)**4.5 - - (17325*(s - t)**3)/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**3.5) - - (17325*(s - t)**3)/ - ((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)**3) - - (13860*(s - t)**3)/ - ((r + Sqrt(r**2 + (s - t)**2))**3* - (r**2 + (s - t)**2)**2.5) - - (6930*(s - t)**3)/ - ((r + Sqrt(r**2 + (s - t)**2))**4* - (r**2 + (s - t)**2)**2) - - (19845*r*(s - t)**5)/(r**2 + (s - t)**2)**5.5 + - (37485*(s - t)**5)/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**4.5) + - (37485*(s - t)**5)/ - ((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)**4) + - (32130*(s - t)**5)/ - ((r + Sqrt(r**2 + (s - t)**2))**3* - (r**2 + (s - t)**2)**3.5) + - (21420*(s - t)**5)/ - ((r + Sqrt(r**2 + (s - t)**2))**4* - (r**2 + (s - t)**2)**3) + - (8568*(s - t)**5)/ - ((r + Sqrt(r**2 + (s - t)**2))**5* - (r**2 + (s - t)**2)**2.5) + - (10395*r*(s - t)**7)/(r**2 + (s - t)**2)**6.5 - - (33075*(s - t)**7)/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**5.5) - - (33075*(s - t)**7)/ - ((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)**5) - - (29400*(s - t)**7)/ - ((r + Sqrt(r**2 + (s - t)**2))**3* - (r**2 + (s - t)**2)**4.5) - - (22050*(s - t)**7)/ - ((r + Sqrt(r**2 + (s - t)**2))**4* - (r**2 + (s - t)**2)**4) - - (12600*(s - t)**7)/ - ((r + Sqrt(r**2 + (s - t)**2))**5* - (r**2 + (s - t)**2)**3.5) - - (4200*(s - t)**7)/ - ((r + Sqrt(r**2 + (s - t)**2))**6* - (r**2 + (s - t)**2)**3) + - (10395*(s - t)**9)/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**6.5) + - (10395*(s - t)**9)/ - ((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)**6) + - (9450*(s - t)**9)/ - ((r + Sqrt(r**2 + (s - t)**2))**3* - (r**2 + (s - t)**2)**5.5) + - (7560*(s - t)**9)/ - ((r + Sqrt(r**2 + (s - t)**2))**4* - (r**2 + (s - t)**2)**5) + - (5040*(s - t)**9)/ - ((r + Sqrt(r**2 + (s - t)**2))**5* - (r**2 + (s - t)**2)**4.5) + - (2520*(s - t)**9)/ - ((r + Sqrt(r**2 + (s - t)**2))**6* - (r**2 + (s - t)**2)**4) + - (720*(s - t)**9)/ - ((r + Sqrt(r**2 + (s - t)**2))**7* - (r**2 + (s - t)**2)**3.5)\ \>", "Output"] }, Open ]], Cell[CellGroupData[{ Cell["D[Out[2],{s,8}]", "Input"], Cell[OutputFormData["\<\ -((5040*(s - t)^10)/ ((r + Sqrt[r^2 + (s - t)^2])^8*(r^2 + (s - t)^2)^4)) - (20160*(s - t)^10)/ ((r + Sqrt[r^2 + (s - t)^2])^7*(r^2 + (s - t)^2)^(9/2)) - (45360*(s - t)^10)/ ((r + Sqrt[r^2 + (s - t)^2])^6*(r^2 + (s - t)^2)^5) - (75600*(s - t)^10)/ ((r + Sqrt[r^2 + (s - t)^2])^5*(r^2 + (s - t)^2)^(11/2)) - (103950*(s - t)^10)/ ((r + Sqrt[r^2 + (s - t)^2])^4*(r^2 + (s - t)^2)^6) - (124740*(s - t)^10)/ ((r + Sqrt[r^2 + (s - t)^2])^3*(r^2 + (s - t)^2)^(13/2)) - (135135*(s - t)^10)/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)^7) - (135135*(s - t)^10)/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(15/2)) + (31680*(s - t)^8)/ ((r + Sqrt[r^2 + (s - t)^2])^7*(r^2 + (s - t)^2)^(7/2)) + (110880*(s - t)^8)/ ((r + Sqrt[r^2 + (s - t)^2])^6*(r^2 + (s - t)^2)^4) + (221760*(s - t)^8)/ ((r + Sqrt[r^2 + (s - t)^2])^5*(r^2 + (s - t)^2)^(9/2)) + (332640*(s - t)^8)/ ((r + Sqrt[r^2 + (s - t)^2])^4*(r^2 + (s - t)^2)^5) + (415800*(s - t)^8)/ ((r + Sqrt[r^2 + (s - t)^2])^3*(r^2 + (s - t)^2)^(11/2)) + (457380*(s - t)^8)/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)^6) + (457380*(s - t)^8)/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(13/2)) - (135135*r*(s - t)^8)/(r^2 + (s - t)^2)^(15/2) - (72240*(s - t)^6)/ ((r + Sqrt[r^2 + (s - t)^2])^6*(r^2 + (s - t)^2)^3) - (216720*(s - t)^6)/ ((r + Sqrt[r^2 + (s - t)^2])^5*(r^2 + (s - t)^2)^(7/2)) - (379260*(s - t)^6)/ ((r + Sqrt[r^2 + (s - t)^2])^4*(r^2 + (s - t)^2)^4) - (505680*(s - t)^6)/ ((r + Sqrt[r^2 + (s - t)^2])^3*(r^2 + (s - t)^2)^(9/2)) - (568890*(s - t)^6)/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)^5) - (568890*(s - t)^6)/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(11/2)) + (291060*r*(s - t)^6)/(r^2 + (s - t)^2)^(13/2) + (70560*(s - t)^4)/ ((r + Sqrt[r^2 + (s - t)^2])^5*(r^2 + (s - t)^2)^(5/2)) + (176400*(s - t)^4)/ ((r + Sqrt[r^2 + (s - t)^2])^4*(r^2 + (s - t)^2)^3) + (264600*(s - t)^4)/ ((r + Sqrt[r^2 + (s - t)^2])^3*(r^2 + (s - t)^2)^(7/2)) + (308700*(s - t)^4)/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)^4) + (308700*(s - t)^4)/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(9/2)) - (198450*r*(s - t)^4)/(r^2 + (s - t)^2)^(11/2) - (25830*(s - t)^2)/ ((r + Sqrt[r^2 + (s - t)^2])^4*(r^2 + (s - t)^2)^2) - (51660*(s - t)^2)/ ((r + Sqrt[r^2 + (s - t)^2])^3*(r^2 + (s - t)^2)^(5/2)) - (64575*(s - t)^2)/ ((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)^3) - (64575*(s - t)^2)/ ((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(7/2)) + (44100*r*(s - t)^2)/(r^2 + (s - t)^2)^(9/2) + 1680/((r + Sqrt[r^2 + (s - t)^2])^3* (r^2 + (s - t)^2)^(3/2)) + 2520/((r + Sqrt[r^2 + (s - t)^2])^2*(r^2 + (s - t)^2)^2) + 2520/((r + Sqrt[r^2 + (s - t)^2])*(r^2 + (s - t)^2)^(5/2)) - (1575*r)/(r^2 + (s - t)^2)^(7/2)\ \>", "\<\ 10 5040 (s - t) -(-------------------------------------------) - 2 2 8 2 2 4 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 10 20160 (s - t) --------------------------------------------- - 2 2 7 2 2 9/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 10 45360 (s - t) ------------------------------------------- - 2 2 6 2 2 5 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 10 75600 (s - t) ---------------------------------------------- - 2 2 5 2 2 11/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 10 103950 (s - t) ------------------------------------------- - 2 2 4 2 2 6 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 10 124740 (s - t) ---------------------------------------------- - 2 2 3 2 2 13/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 10 135135 (s - t) ------------------------------------------- - 2 2 2 2 2 7 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 10 135135 (s - t) --------------------------------------------- + 2 2 2 2 15/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 8 31680 (s - t) --------------------------------------------- + 2 2 7 2 2 7/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 8 110880 (s - t) ------------------------------------------- + 2 2 6 2 2 4 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 8 221760 (s - t) --------------------------------------------- + 2 2 5 2 2 9/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 8 332640 (s - t) ------------------------------------------- + 2 2 4 2 2 5 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 8 415800 (s - t) ---------------------------------------------- + 2 2 3 2 2 11/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 8 457380 (s - t) ------------------------------------------- + 2 2 2 2 2 6 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 8 457380 (s - t) --------------------------------------------- - 2 2 2 2 13/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 8 135135 r (s - t) ------------------- - 2 2 15/2 (r + (s - t) ) 6 72240 (s - t) ------------------------------------------- - 2 2 6 2 2 3 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 6 216720 (s - t) --------------------------------------------- - 2 2 5 2 2 7/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 6 379260 (s - t) ------------------------------------------- - 2 2 4 2 2 4 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 6 505680 (s - t) --------------------------------------------- - 2 2 3 2 2 9/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 6 568890 (s - t) ------------------------------------------- - 2 2 2 2 2 5 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 6 568890 (s - t) --------------------------------------------- + 2 2 2 2 11/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 6 291060 r (s - t) ------------------- + 2 2 13/2 (r + (s - t) ) 4 70560 (s - t) --------------------------------------------- + 2 2 5 2 2 5/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 4 176400 (s - t) ------------------------------------------- + 2 2 4 2 2 3 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 4 264600 (s - t) --------------------------------------------- + 2 2 3 2 2 7/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 4 308700 (s - t) ------------------------------------------- + 2 2 2 2 2 4 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 4 308700 (s - t) -------------------------------------------- - 2 2 2 2 9/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 4 198450 r (s - t) ------------------- - 2 2 11/2 (r + (s - t) ) 2 25830 (s - t) ------------------------------------------- - 2 2 4 2 2 2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 2 51660 (s - t) --------------------------------------------- - 2 2 3 2 2 5/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 2 64575 (s - t) ------------------------------------------- - 2 2 2 2 2 3 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 2 64575 (s - t) -------------------------------------------- + 2 2 2 2 7/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 2 44100 r (s - t) ------------------ + 2 2 9/2 (r + (s - t) ) 1680 --------------------------------------------- + 2 2 3 2 2 3/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 2520 ------------------------------------------- + 2 2 2 2 2 2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 2520 -------------------------------------------- - 2 2 2 2 5/2 (r + Sqrt[r + (s - t) ]) (r + (s - t) ) 1575 r ------------------ 2 2 7/2 (r + (s - t) )\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["FortranForm[%]", "Input"], Cell["\<\ (-1575*r)/(r**2 + (s - t)**2)**3.5 + - 2520/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**2.5) + - 2520/ - ((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)**2) + - 1680/ - ((r + Sqrt(r**2 + (s - t)**2))**3* - (r**2 + (s - t)**2)**1.5) + - (44100*r*(s - t)**2)/(r**2 + (s - t)**2)**4.5 - - (64575*(s - t)**2)/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**3.5) - - (64575*(s - t)**2)/ - ((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)**3) - - (51660*(s - t)**2)/ - ((r + Sqrt(r**2 + (s - t)**2))**3* - (r**2 + (s - t)**2)**2.5) - - (25830*(s - t)**2)/ - ((r + Sqrt(r**2 + (s - t)**2))**4* - (r**2 + (s - t)**2)**2) - - (198450*r*(s - t)**4)/(r**2 + (s - t)**2)**5.5 + - (308700*(s - t)**4)/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**4.5) + - (308700*(s - t)**4)/ - ((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)**4) + - (264600*(s - t)**4)/ - ((r + Sqrt(r**2 + (s - t)**2))**3* - (r**2 + (s - t)**2)**3.5) + - (176400*(s - t)**4)/ - ((r + Sqrt(r**2 + (s - t)**2))**4* - (r**2 + (s - t)**2)**3) + - (70560*(s - t)**4)/ - ((r + Sqrt(r**2 + (s - t)**2))**5* - (r**2 + (s - t)**2)**2.5) + - (291060*r*(s - t)**6)/(r**2 + (s - t)**2)**6.5 - - (568890*(s - t)**6)/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**5.5) - - (568890*(s - t)**6)/ - ((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)**5) - - (505680*(s - t)**6)/ - ((r + Sqrt(r**2 + (s - t)**2))**3* - (r**2 + (s - t)**2)**4.5) - - (379260*(s - t)**6)/ - ((r + Sqrt(r**2 + (s - t)**2))**4* - (r**2 + (s - t)**2)**4) - - (216720*(s - t)**6)/ - ((r + Sqrt(r**2 + (s - t)**2))**5* - (r**2 + (s - t)**2)**3.5) - - (72240*(s - t)**6)/ - ((r + Sqrt(r**2 + (s - t)**2))**6* - (r**2 + (s - t)**2)**3) - - (135135*r*(s - t)**8)/(r**2 + (s - t)**2)**7.5 + - (457380*(s - t)**8)/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**6.5) + - (457380*(s - t)**8)/ - ((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)**6) + - (415800*(s - t)**8)/ - ((r + Sqrt(r**2 + (s - t)**2))**3* - (r**2 + (s - t)**2)**5.5) + - (332640*(s - t)**8)/ - ((r + Sqrt(r**2 + (s - t)**2))**4* - (r**2 + (s - t)**2)**5) + - (221760*(s - t)**8)/ - ((r + Sqrt(r**2 + (s - t)**2))**5* - (r**2 + (s - t)**2)**4.5) + - (110880*(s - t)**8)/ - ((r + Sqrt(r**2 + (s - t)**2))**6* - (r**2 + (s - t)**2)**4) + - (31680*(s - t)**8)/ - ((r + Sqrt(r**2 + (s - t)**2))**7* - (r**2 + (s - t)**2)**3.5) - - (135135*(s - t)**10)/ - ((r + Sqrt(r**2 + (s - t)**2))* - (r**2 + (s - t)**2)**7.5) - - (135135*(s - t)**10)/ - ((r + Sqrt(r**2 + (s - t)**2))**2* - (r**2 + (s - t)**2)**7) - - (124740*(s - t)**10)/ - ((r + Sqrt(r**2 + (s - t)**2))**3* - (r**2 + (s - t)**2)**6.5) - - (103950*(s - t)**10)/ - ((r + Sqrt(r**2 + (s - t)**2))**4* - (r**2 + (s - t)**2)**6) - - (75600*(s - t)**10)/ - ((r + Sqrt(r**2 + (s - t)**2))**5* - (r**2 + (s - t)**2)**5.5) - - (45360*(s - t)**10)/ - ((r + Sqrt(r**2 + (s - t)**2))**6* - (r**2 + (s - t)**2)**5) - - (20160*(s - t)**10)/ - ((r + Sqrt(r**2 + (s - t)**2))**7* - (r**2 + (s - t)**2)**4.5) - - (5040*(s - t)**10)/ - ((r + Sqrt(r**2 + (s - t)**2))**8* - (r**2 + (s - t)**2)**4)\ \>", "Output"] }, Open ]] }, FrontEndVersion->"X 3.0", ScreenRectangle->{{0, 1280}, {0, 1024}}, WindowSize->{520, 600}, WindowMargins->{{324, Automatic}, {138, Automatic}} ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. ***********************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1731, 51, 70, 0, 27, "Input"], Cell[1804, 53, 246, 7, 34, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[2087, 65, 26, 0, 27, "Input"], Cell[2116, 67, 641, 16, 104, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[2794, 88, 31, 0, 27, "Input"], Cell[2828, 90, 212, 5, 99, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[3077, 100, 32, 0, 27, "Input"], Cell[3112, 102, 1228, 39, 262, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[4377, 146, 31, 0, 27, "Input"], Cell[4411, 148, 439, 11, 204, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[4887, 164, 32, 0, 27, "Input"], Cell[4922, 166, 1944, 62, 410, "Output"] }, Open ]], Cell[6881, 231, 63, 4, 25, "Input"], Cell[6947, 237, 63, 4, 25, "Input"], Cell[CellGroupData[{ Cell[7035, 245, 36, 0, 27, "Input"], Cell[7074, 247, 734, 19, 324, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[7845, 271, 32, 0, 27, "Input"], Cell[7880, 273, 3208, 99, 673, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[11125, 377, 31, 0, 27, "Input"], Cell[11159, 379, 1205, 32, 504, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[12401, 416, 32, 0, 27, "Input"], Cell[12436, 418, 4344, 132, 874, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[16817, 555, 31, 0, 27, "Input"], Cell[16851, 557, 1675, 45, 699, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[18563, 607, 32, 0, 27, "Input"], Cell[18598, 609, 6192, 184, 1242, "Output"] }, Open ]], Cell[24805, 796, 63, 4, 25, "Input"], Cell[CellGroupData[{ Cell[24893, 804, 31, 0, 27, "Input"], Cell[24927, 806, 2357, 63, 954, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[27321, 874, 32, 0, 27, "Input"], Cell[27356, 876, 7701, 226, 1495, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[35094, 1107, 31, 0, 27, "Input"], Cell[35128, 1109, 2989, 80, 1209, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[38154, 1194, 32, 0, 27, "Input"], Cell[38189, 1196, 10199, 294, 1968, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[48425, 1495, 31, 0, 27, "Input"], Cell[48459, 1497, 3931, 105, 1584, "Output"] }, Open ]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)