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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=-7/4, b>=a > For fixed z and a=-7/4, b=-3/2





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









  


  








Input Form





Hypergeometric2F1[-(7/4), -(3/2), 6, z] == (128 Sqrt[2] (2 (1 - z)^(1/4) (8192 - 86784 z + 441936 z^2 - 1530224 z^3 + 5004516 z^4 + 19155114 z^5 + 3444375 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (8192 - 86784 z + 441936 z^2 - 1530224 z^3 + 5004516 z^4 + 19155114 z^5 + 3444375 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (8192 - 86784 z + 441936 z^2 - 1530224 z^3 + 5004516 z^4 + 19155114 z^5 + 3444375 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (8192 - 86784 z + 441936 z^2 - 1530224 z^3 + 5004516 z^4 + 19155114 z^5 + 3444375 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (8192 - 86784 z + 441936 z^2 - 1530224 z^3 + 5004516 z^4 + 19155114 z^5 + 3444375 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-8192 + 90880 z - 484560 z^2 + 1743440 z^3 - 5732020 z^4 + 13671702 z^5 + 16057635 z^6 + 1098240 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (1948781835 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