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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=-11/2, b>=a > For fixed z and a=-11/2, b=-15/4





http://functions.wolfram.com/07.23.03.a7wz.01









  


  








Input Form





Hypergeometric2F1[-(11/2), -(15/4), 4, z] == (2 (1 - z)^(1/4) (157696 - 4464768 z + 95889024 z^2 + 4511115968 z^3 + 15484866720 z^4 + 12940622424 z^5 + 2646407808 z^6 + 56328426 z^7 - 908523 z^8) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (157696 - 4464768 z + 95889024 z^2 + 4511115968 z^3 + 15484866720 z^4 + 12940622424 z^5 + 2646407808 z^6 + 56328426 z^7 - 908523 z^8) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-157696 + 4543616 z - 98106624 z^2 - 447910976 z^3 + 6983324320 z^4 + 18091754856 z^5 + 10020213144 z^6 + 1176051294 z^7 + 302841 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (-157696 + 4464768 z - 95889024 z^2 - 4511115968 z^3 - 15484866720 z^4 - 12940622424 z^5 - 2646407808 z^6 - 56328426 z^7 + 908523 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (-157696 + 4464768 z - 95889024 z^2 - 4511115968 z^3 - 15484866720 z^4 - 12940622424 z^5 - 2646407808 z^6 - 56328426 z^7 + 908523 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (-157696 + 4464768 z - 95889024 z^2 - 4511115968 z^3 - 15484866720 z^4 - 12940622424 z^5 - 2646407808 z^6 - 56328426 z^7 + 908523 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (1003917915 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z^3)








Standard Form





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MathML Form







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Rule Form





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





2007-05-02