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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 4 and fixed z > For fixed z and a=-17/4, b>=a > For fixed z and a=-17/4, b=-1/2





http://functions.wolfram.com/07.23.03.aag2.01









  


  








Input Form





Hypergeometric2F1[-(17/4), -(1/2), 5, z] == (128 Sqrt[2] (-2 (56576 - 693056 z + 4357236 z^2 - 22616256 z^3 - 262431945 z^4 - 54824448 z^5 + 8776768 z^6 - 1310848 z^7 + 103488 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (56576 - 693056 z + 4357236 z^2 - 22616256 z^3 - 262431945 z^4 - 54824448 z^5 + 8776768 z^6 - 1310848 z^7 + 103488 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (-56576 + 664768 z - 4033692 z^2 + 20698860 z^3 + 90032055 z^4 + 2596608 z^5 - 409024 z^6 + 34496 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (56576 - 693056 z + 4357236 z^2 - 22616256 z^3 - 262431945 z^4 - 54824448 z^5 + 8776768 z^6 - 1310848 z^7 + 103488 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (56576 - 693056 z + 4357236 z^2 - 22616256 z^3 - 262431945 z^4 - 54824448 z^5 + 8776768 z^6 - 1310848 z^7 + 103488 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (56576 - 693056 z + 4357236 z^2 - 22616256 z^3 - 262431945 z^4 - 54824448 z^5 + 8776768 z^6 - 1310848 z^7 + 103488 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (11658772125 Pi Sqrt[1 + Sqrt[1 - z]] z^4)








Standard Form





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MathML Form







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





2007-05-02