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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=13/8, b>=a > For fixed z and a=13/8, b=39/8





http://functions.wolfram.com/07.23.03.c4o7.01









  


  










Input Form





Hypergeometric2F1[13/8, 39/8, 6, z] == (1/(140821065 Pi z^5)) (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-32768 + 1920 z + 765 z^2 + 300 z^3) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 20 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1024 + 108 z + 45 z^2 + 30 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (1/Sqrt[1 - z]) (3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-4096 + 1360 z + 555 z^2 + 300 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]) - 2 (-32768 + 1920 z + 765 z^2 + 300 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - 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