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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=5/2





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









  


  








Input Form





Hypergeometric2F1[-(17/4), 5/2, 5, z] == (1024 Sqrt[2] (2 (-21216 + 84864 z - 69615 z^2 - 88179 z^3 + 1023885 z^4 - 1801797 z^5 + 1479203 z^6 - 607145 z^7 + 100947 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-21216 + 84864 z - 69615 z^2 - 88179 z^3 + 1023885 z^4 - 1801797 z^5 + 1479203 z^6 - 607145 z^7 + 100947 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (21216 - 74256 z + 35802 z^2 + 96135 z^3 - 324420 z^4 + 353367 z^5 - 175142 z^6 + 33649 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (-21216 + 84864 z - 69615 z^2 - 88179 z^3 + 1023885 z^4 - 1801797 z^5 + 1479203 z^6 - 607145 z^7 + 100947 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (-21216 + 84864 z - 69615 z^2 - 88179 z^3 + 1023885 z^4 - 1801797 z^5 + 1479203 z^6 - 607145 z^7 + 100947 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (-21216 + 84864 z - 69615 z^2 - 88179 z^3 + 1023885 z^4 - 1801797 z^5 + 1479203 z^6 - 607145 z^7 + 100947 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (333107775 Pi Sqrt[1 + Sqrt[1 - z]] z^4)








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