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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=-9/2, b>=a > For fixed z and a=-9/2, b=11/4





http://functions.wolfram.com/07.23.03.aa3q.01









  


  








Input Form





Hypergeometric2F1[-(9/2), 11/4, 5, z] == (8 Sqrt[2] (2 (-36864 + 125952 z - 47040 z^2 - 100800 z^3 + 800480 z^4 - 1407872 z^5 + 1174836 z^6 - 490620 z^7 + 82875 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-36864 + 125952 z - 47040 z^2 - 100800 z^3 + 800480 z^4 - 1407872 z^5 + 1174836 z^6 - 490620 z^7 + 82875 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (-36864 + 125952 z - 47040 z^2 - 100800 z^3 + 800480 z^4 - 1407872 z^5 + 1174836 z^6 - 490620 z^7 + 82875 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (-36864 + 125952 z - 47040 z^2 - 100800 z^3 + 800480 z^4 - 1407872 z^5 + 1174836 z^6 - 490620 z^7 + 82875 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (-36864 + 125952 z - 47040 z^2 - 100800 z^3 + 800480 z^4 - 1407872 z^5 + 1174836 z^6 - 490620 z^7 + 82875 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (36864 - 107520 z - 960 z^2 + 86400 z^3 + 193120 z^4 - 735488 z^5 + 835380 z^6 - 424320 z^7 + 82875 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (3828825 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