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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For rational parameters with denominators 4 and fixed z > For fixed z and a=-13/4, b>=a > For fixed z and a=-13/4, b=19/4





http://functions.wolfram.com/07.23.03.acsh.01









  


  








Input Form





Hypergeometric2F1[-(13/4), 19/4, -(11/2), z] == (1/(4553472 Pi^(3/2))) (((1/(-1 + z)^7) (2 (-1138368 + 4631088 z - 5609912 z^2 + 698775 z^3 + 578347 z^4 + 973973 z^5 + 4710321 z^6 - 17457344 z^7 + 19658240 z^8 - 9732096 z^9 + 1835008 z^10) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^7) (2 (-1138368 + 4631088 z - 5609912 z^2 + 698775 z^3 + 578347 z^4 + 973973 z^5 + 4710321 z^6 - 17457344 z^7 + 19658240 z^8 - 9732096 z^9 + 1835008 z^10) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^6)) ((1138368 - 569184 Sqrt[z] - 4061904 z + 1793792 z^(3/2) + 3816120 z^2 - 1180410 z^(5/2) + 481635 z^3 - 678370 z^(7/2) + 100023 z^4 - 352814 z^(9/2) - 621159 z^5 + 134442 z^(11/2) - 4844763 z^6 + 8151104 z^(13/2) + 9306240 z^7 - 13606400 z^(15/2) - 6051840 z^8 + 8355840 z^(17/2) + 1376256 z^9 - 1835008 z^(19/2)) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^7)) ((1138368 + 569184 Sqrt[z] - 4061904 z - 1793792 z^(3/2) + 3816120 z^2 + 1180410 z^(5/2) + 481635 z^3 + 678370 z^(7/2) + 100023 z^4 + 352814 z^(9/2) - 621159 z^5 - 134442 z^(11/2) - 4844763 z^6 - 8151104 z^(13/2) + 9306240 z^7 + 13606400 z^(15/2) - 6051840 z^8 - 8355840 z^(17/2) + 1376256 z^9 + 1835008 z^(19/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)








Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2007-05-02