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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.a82l.01









  


  








Input Form





Hypergeometric2F1[-(11/2), 15/4, 2, z] == (-2 (20160 - 1808224 z + 13369312 z^2 - 36793440 z^3 + 47802300 z^4 - 29801850 z^5 + 7210125 z^6) EllipticE[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (20160 - 1808224 z + 13369312 z^2 - 36793440 z^3 + 47802300 z^4 - 29801850 z^5 + 7210125 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (20160 - 356704 z - 1490560 z^2 + 13578240 z^3 - 28575300 z^4 + 24033750 z^5 - 7210125 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (20160 - 1808224 z + 13369312 z^2 - 36793440 z^3 + 47802300 z^4 - 29801850 z^5 + 7210125 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (20160 - 1808224 z + 13369312 z^2 - 36793440 z^3 + 47802300 z^4 - 29801850 z^5 + 7210125 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (20160 - 1808224 z + 13369312 z^2 - 36793440 z^3 + 47802300 z^4 - 29801850 z^5 + 7210125 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (360360 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z)








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