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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=15/4





http://functions.wolfram.com/07.23.03.a8s0.01









  


  










Input Form





Hypergeometric2F1[-(21/4), 15/4, 1, -z] == (1/(765765 Pi Sqrt[1 + Sqrt[1 + z]])) (2 Sqrt[2] ((1578683 + 23802607 z + 100703360 z^2 + 178432000 z^3 + 141885440 z^4 + 41943040 z^5) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + Sqrt[1 + z] (1578683 + 23802607 z + 100703360 z^2 + 178432000 z^3 + 141885440 z^4 + 41943040 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 2 Sqrt[1 + z] (406459 + 4333480 z + 12648960 z^2 + 13967360 z^3 + 5242880 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (1578683 + 23802607 z + 100703360 z^2 + 178432000 z^3 + 141885440 z^4 + 41943040 z^5) 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