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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=-1/4, b>=a > For fixed z and a=-1/4, b=23/4





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









  


  








Input Form





Hypergeometric2F1[-(1/4), 23/4, 4, -z] == (256 Sqrt[2] (((224 - 791 z + 3276 z^2 + 45056 z^3 + 40960 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z) + ((224 - 791 z + 3276 z^2 + 45056 z^3 + 40960 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/Sqrt[1 + z] - ((224 - 623 z + 2667 z^2 + 14144 z^3 + 10240 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^(3/2) - ((224 - 791 z + 3276 z^2 + 45056 z^3 + 40960 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)))/ (4279275 Pi z^3 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