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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=-7/4, b>=a > For fixed z and a=-7/4, b=13/4





http://functions.wolfram.com/07.23.03.af75.01









  


  








Input Form





Hypergeometric2F1[-(7/4), 13/4, -(11/2), z] == (1/(31680 Pi^(3/2))) (((1/(-1 + z)^7) (2 Sqrt[z] (-15840 + 88560 z - 191982 z^2 + 186921 z^3 - 51975 z^4 - 26565 z^5 + 160545 z^6 - 106656 z^7 + 22528 z^8) EllipticE[(1/2) (1 - Sqrt[z])]) - (1/(-1 + z)^7) (2 Sqrt[z] (-15840 + 88560 z - 191982 z^2 + 186921 z^3 - 51975 z^4 - 26565 z^5 + 160545 z^6 - 106656 z^7 + 22528 z^8) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^6)) ((-31680 + 47520 Sqrt[z] + 153360 z - 241920 z^(3/2) - 271320 z^2 + 463302 z^(5/2) + 180369 z^3 - 367290 z^(7/2) + 17325 z^4 + 34650 z^(9/2) - 35805 z^5 + 62370 z^(11/2) - 95865 z^6 - 64680 z^(13/2) + 89760 z^7 + 16896 z^(15/2) - 22528 z^8) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^7)) ((31680 + 47520 Sqrt[z] - 153360 z - 241920 z^(3/2) + 271320 z^2 + 463302 z^(5/2) - 180369 z^3 - 367290 z^(7/2) - 17325 z^4 + 34650 z^(9/2) + 35805 z^5 + 62370 z^(11/2) + 95865 z^6 - 64680 z^(13/2) - 89760 z^7 + 16896 z^(15/2) + 22528 z^8) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)








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