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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=-3/8, b>=a > For fixed z and a=-3/8, b=15/8





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









  


  










Input Form





Hypergeometric2F1[-(3/8), 15/8, 6, z] == (1/(15159496275 Pi z^5)) (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-98304 + 408192 z - 622057 z^2 + 381264 z^3 - 19125 z^4 + 12750 z^5) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 6 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (6144 - 21048 z + 24019 z^2 - 7650 z^3 + 6375 z^4) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (12288 - 49008 z + 70331 z^2 - 38250 z^3 - 13005 z^4 + 5100 z^5) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (-98304 + 408192 z - 622057 z^2 + 381264 z^3 - 19125 z^4 + 12750 z^5) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))










Standard Form





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MathML Form







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</annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02