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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.a81q.01









  


  








Input Form





Hypergeometric2F1[-(11/2), 11/4, 3, z] == (-2 (8448 + 48576 z - 1118208 z^2 + 4098656 z^3 - 6784496 z^4 + 5900700 z^5 - 2638740 z^6 + 480675 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (8448 + 48576 z - 1118208 z^2 + 4098656 z^3 - 6784496 z^4 + 5900700 z^5 - 2638740 z^6 + 480675 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (8448 + 52800 z - 9408 z^2 - 1212448 z^3 + 3482960 z^4 - 4097340 z^5 + 2254200 z^6 - 480675 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (8448 + 48576 z - 1118208 z^2 + 4098656 z^3 - 6784496 z^4 + 5900700 z^5 - 2638740 z^6 + 480675 z^7) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (8448 + 48576 z - 1118208 z^2 + 4098656 z^3 - 6784496 z^4 + 5900700 z^5 - 2638740 z^6 + 480675 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (8448 + 48576 z - 1118208 z^2 + 4098656 z^3 - 6784496 z^4 + 5900700 z^5 - 2638740 z^6 + 480675 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (270270 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z^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