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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=-17/4, b>=a > For fixed z and a=-17/4, b=7/2





http://functions.wolfram.com/07.23.03.aas1.01









  


  








Input Form





Hypergeometric2F1[-(17/4), 7/2, 4, z] == (32 Sqrt[2] (2 (-21216 - 41106 z - 186303 z^2 + 5511065 z^3 - 16786150 z^4 + 21040448 z^5 - 12214587 z^6 + 2725569 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-21216 - 41106 z - 186303 z^2 + 5511065 z^3 - 16786150 z^4 + 21040448 z^5 - 12214587 z^6 + 2725569 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (21216 + 51714 z + 215475 z^2 - 2239160 z^3 + 4369050 z^4 - 3336058 z^5 + 908523 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (-21216 - 41106 z - 186303 z^2 + 5511065 z^3 - 16786150 z^4 + 21040448 z^5 - 12214587 z^6 + 2725569 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (-21216 - 41106 z - 186303 z^2 + 5511065 z^3 - 16786150 z^4 + 21040448 z^5 - 12214587 z^6 + 2725569 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (-21216 - 41106 z - 186303 z^2 + 5511065 z^3 - 16786150 z^4 + 21040448 z^5 - 12214587 z^6 + 2725569 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (50470875 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