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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=-5/4, b>=a > For fixed z and a=-5/4, b=5/2





http://functions.wolfram.com/07.23.03.ag2t.01









  


  








Input Form





Hypergeometric2F1[-(5/4), 5/2, 6, z] == (2048 Sqrt[2] (-2 (-512 + 1936 z - 2405 z^2 + 700 z^3 + 400 z^4 - 1274 z^5 + 462 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (-512 + 1936 z - 2405 z^2 + 700 z^3 + 400 z^4 - 1274 z^5 + 462 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (512 - 1680 z + 1645 z^2 - 100 z^3 - 300 z^4 + 154 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (-512 + 1936 z - 2405 z^2 + 700 z^3 + 400 z^4 - 1274 z^5 + 462 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (-512 + 1936 z - 2405 z^2 + 700 z^3 + 400 z^4 - 1274 z^5 + 462 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (-512 + 1936 z - 2405 z^2 + 700 z^3 + 400 z^4 - 1274 z^5 + 462 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (1044225 Pi Sqrt[1 + Sqrt[1 - z]] z^5)








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