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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=-5/2, b>=a > For fixed z and a=-5/2, b=-9/4





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Input Form





Hypergeometric2F1[-(5/2), -(9/4), 2, z] == (2 (1 + Sqrt[1 - z]) (360 + 29984 z + 58918 z^2 + 11685 z^3) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (360 (1 + (1 - z)^(1/4) + Sqrt[1 - z] + (1 - z)^(3/4)) + 8 (3748 + 3748 (1 - z)^(1/4) + 3748 Sqrt[1 - z] + 1723 (1 - z)^(3/4)) z + 2 (29459 + 29459 (1 - z)^(1/4) + 29459 Sqrt[1 - z] + 8875 (1 - z)^(3/4)) z^2 + 15 (779 + 779 (1 - z)^(1/4) + 779 Sqrt[1 - z] + 117 (1 - z)^(3/4)) z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (4095 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] 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