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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=1/8, b>=a > For fixed z and a=1/8, b=27/8





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









  


  










Input Form





Hypergeometric2F1[1/8, 27/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[1 - z] (32768 - 46976 z + 4355 z^2 + 3445 z^3 + 3900 z^4) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (32768 - 46976 z + 4355 z^2 + 3445 z^3 + 3900 z^4) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (32768 - 46976 z + 4355 z^2 + 3445 z^3 + 3900 z^4) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (32768 - 67456 z + 30355 z^2 + 3965 z^3 + 2600 z^4 + 7800 z^5) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (2644306665 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^5)










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