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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=-3/4, b>=a > For fixed z and a=-3/4, b=-3/4





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









  


  








Input Form





Hypergeometric2F1[-(3/4), -(3/4), 5, -z] == (4096 Sqrt[2] (2 Sqrt[1 + z] (-192 - 1336 z - 4347 z^2 - 10494 z^3 + 11189 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 2 (-192 - 1528 z - 5683 z^2 - 14841 z^3 + 695 z^4 + 11189 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 2 Sqrt[1 + z] (-192 - 1336 z - 4347 z^2 - 10494 z^3 + 11189 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-384 - 2960 z - 10671 z^2 - 27333 z^3 - 71213 z^4 + 21945 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (160527675 Pi z^4 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