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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=-21/4, b>=a > For fixed z and a=-21/4, b=-21/4





http://functions.wolfram.com/07.23.03.a856.01









  


  










Input Form





Hypergeometric2F1[-(21/4), -(21/4), 2, -z] == (1/(8701875 Pi z Sqrt[1 + Sqrt[1 + z]])) (8 Sqrt[2] ((-(13923 - 5959378 z + 68186425 z^2 - 176838700 z^3 + 133509925 z^4 - 27916258 z^5 + 1054303 z^6)) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (13923 - 5959378 z + 68186425 z^2 - 176838700 z^3 + 133509925 z^4 - 27916258 z^5 + 1054303 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (13923 - 3787390 z + 38746325 z^2 - 90884100 z^3 + 61649725 z^4 - 11309918 z^5 + 348075 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (13923 - 5959378 z + 68186425 z^2 - 176838700 z^3 + 133509925 z^4 - 27916258 z^5 + 1054303 z^6) EllipticK[(-1 + Sqrt[1 + z])/ (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