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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 8 and fixed z and a<0 > For fixed z and a=-21/8, b>=a > For fixed z and a=-21/8, b=-7/8





http://functions.wolfram.com/07.23.03.bla9.01









  


  










Input Form





Hypergeometric2F1[-(21/8), -(7/8), 4, z] == (2048 2^(1/4) (-2 Sqrt[1 - z] (-11648 + 120575 z - 779415 z^2 - 4057045 z^3 - 573965 z^4 + 29946 z^5) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-11648 + 120575 z - 779415 z^2 - 4057045 z^3 - 573965 z^4 + 29946 z^5) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (-11648 + 127855 z - 853580 z^2 + 11715530 z^3 + 10103060 z^4 + 4991 z^5) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (-11648 + 120575 z - 779415 z^2 - 4057045 z^3 - 573965 z^4 + 29946 z^5) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/(15664378275 Pi Sqrt[Sqrt[2] + 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