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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=9/2





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









  


  








Input Form





Hypergeometric2F1[-(17/4), 9/2, 5, z] == (256 Sqrt[2] (2 (-84864 - 127296 z - 336804 z^2 - 1701921 z^3 + 53329505 z^4 - 166865258 z^5 + 212825118 z^6 - 125073333 z^7 + 28164213 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-84864 - 127296 z - 336804 z^2 - 1701921 z^3 + 53329505 z^4 - 166865258 z^5 + 212825118 z^6 - 125073333 z^7 + 28164213 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (84864 + 169728 z + 434928 z^2 + 1952535 z^3 - 21906620 z^4 + 43924618 z^5 - 34091244 z^6 + 9388071 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (-84864 - 127296 z - 336804 z^2 - 1701921 z^3 + 53329505 z^4 - 166865258 z^5 + 212825118 z^6 - 125073333 z^7 + 28164213 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (-84864 - 127296 z - 336804 z^2 - 1701921 z^3 + 53329505 z^4 - 166865258 z^5 + 212825118 z^6 - 125073333 z^7 + 28164213 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (-84864 - 127296 z - 336804 z^2 - 1701921 z^3 + 53329505 z^4 - 166865258 z^5 + 212825118 z^6 - 125073333 z^7 + 28164213 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (3886257375 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