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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=11/4





http://functions.wolfram.com/07.23.03.a81r.01









  


  








Input Form





Hypergeometric2F1[-(11/2), 11/4, 4, z] == (-2 (-67584 + 63360 z + 206976 z^2 - 2904256 z^3 + 8019936 z^4 - 10693544 z^5 + 7796880 z^6 - 3003390 z^7 + 480675 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (-67584 + 63360 z + 206976 z^2 - 2904256 z^3 + 8019936 z^4 - 10693544 z^5 + 7796880 z^6 - 3003390 z^7 + 480675 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (-67584 + 29568 z + 211200 z^2 + 263744 z^3 - 3015392 z^4 + 6108440 z^5 - 5701800 z^6 + 2618850 z^7 - 480675 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (-67584 + 63360 z + 206976 z^2 - 2904256 z^3 + 8019936 z^4 - 10693544 z^5 + 7796880 z^6 - 3003390 z^7 + 480675 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (-67584 + 63360 z + 206976 z^2 - 2904256 z^3 + 8019936 z^4 - 10693544 z^5 + 7796880 z^6 - 3003390 z^7 + 480675 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (-67584 + 63360 z + 206976 z^2 - 2904256 z^3 + 8019936 z^4 - 10693544 z^5 + 7796880 z^6 - 3003390 z^7 + 480675 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (765765 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