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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=-5/4, b>=a > For fixed z and a=-5/4, b=23/4





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









  


  










Input Form





Hypergeometric2F1[-(5/4), 23/4, 1, -z] == (1/(21945 Pi Sqrt[1 + Sqrt[1 + z]])) (2 Sqrt[2] (((41397 + 317649 z + 708480 z^2 + 628736 z^3 + 196608 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^3 + ((41397 + 317649 z + 708480 z^2 + 628736 z^3 + 196608 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^(5/2) - (4 (4863 + 28197 z + 53748 z^2 + 42752 z^3 + 12288 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^(7/2) - ((41397 + 317649 z + 708480 z^2 + 628736 z^3 + 196608 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^3))










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