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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=17/8, b>=a > For fixed z and a=17/8, b=43/8





http://functions.wolfram.com/07.23.03.c6ph.01









  


  










Input Form





Hypergeometric2F1[17/8, 43/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[1 - z] (32768 - 38784 z + 1539 z^2 + 717 z^3 + 540 z^4) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (32768 - 38784 z + 1539 z^2 + 717 z^3 + 540 z^4) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (32768 - 38784 z + 1539 z^2 + 717 z^3 + 540 z^4) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (-1 + z) (-32768 + 26496 z + 4077 z^2 + 1920 z^3 + 1080 z^4) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (286184745 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] (-1 + z)^2 z^5)










Standard Form





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MathML Form







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</semantics> </math>










Rule Form





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





2007-05-02