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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=-7/2, b>=a > For fixed z and a=-7/2, b=11/4





http://functions.wolfram.com/07.23.03.ac2b.01









  


  








Input Form





Hypergeometric2F1[-(7/2), 11/4, 5, z] == (1/(225225 Pi Sqrt[1 + Sqrt[1 - z]] z^4)) (16 Sqrt[2] (-2 (2048 - 6144 z + 1920 z^2 + 3600 z^3 - 21920 z^4 + 28704 z^5 - 15912 z^6 + 3315 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (2048 - 6144 z + 1920 z^2 + 3600 z^3 - 21920 z^4 + 28704 z^5 - 15912 z^6 + 3315 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (2048 - 6144 z + 1920 z^2 + 3600 z^3 - 21920 z^4 + 28704 z^5 - 15912 z^6 + 3315 z^7) EllipticK[1/2 - (1 - z)^(1/4)/ (1 + Sqrt[1 - z])] + (1 - z)^(1/4) (2048 - 6144 z + 1920 z^2 + 3600 z^3 - 21920 z^4 + 28704 z^5 - 15912 z^6 + 3315 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (2048 - 6144 z + 1920 z^2 + 3600 z^3 - 21920 z^4 + 28704 z^5 - 15912 z^6 + 3315 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (-2048 + 5120 z + 320 z^2 - 2800 z^3 - 7280 z^4 + 18096 z^5 - 13260 z^6 + 3315 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(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