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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=-13/4, b>=a > For fixed z and a=-13/4, b=23/4





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









  


  








Input Form





Hypergeometric2F1[-(13/4), 23/4, 3, -z] == (64 Sqrt[2] ((-1716 + 33891 z + 2315904 z^2 + 11307008 z^3 + 17367040 z^4 + 8388608 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (-1716 + 33891 z + 2315904 z^2 + 11307008 z^3 + 17367040 z^4 + 8388608 z^5) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - 4 Sqrt[1 + z] (-429 + 8580 z + 235776 z^2 + 708608 z^3 + 524288 z^4) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - (-1716 + 33891 z + 2315904 z^2 + 11307008 z^3 + 17367040 z^4 + 8388608 z^5) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])]))/(43648605 Pi z^2 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