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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=19/4





http://functions.wolfram.com/07.23.03.ag9t.01









  


  








Input Form





Hypergeometric2F1[-(5/4), 19/4, -(9/2), z] == (1/(1862784 Pi^(3/2))) (((1/(-1 + z)^8) (4 (232848 - 1526448 z + 3945711 z^2 - 4559786 z^3 + 882882 z^4 + 2018016 z^5 - 3943641 z^6 + 2951442 z^7 - 1078272 z^8 + 159744 z^9) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^8) (4 (232848 - 1526448 z + 3945711 z^2 - 4559786 z^3 + 882882 z^4 + 2018016 z^5 - 3943641 z^6 + 2951442 z^7 - 1078272 z^8 + 159744 z^9) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^8 (1 + Sqrt[z])^7)) ((-465696 + 232848 Sqrt[z] + 2820048 z - 1313004 z^(3/2) - 6578418 z^2 + 2750209 z^(5/2) + 6369363 z^3 - 2081079 z^(7/2) + 315315 z^4 - 945945 z^(9/2) - 3090087 z^5 + 4720911 z^(11/2) + 3166371 z^6 - 4502628 z^(13/2) - 1400256 z^7 + 1916928 z^(15/2) + 239616 z^8 - 319488 z^(17/2)) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^8)) ((-465696 - 232848 Sqrt[z] + 2820048 z + 1313004 z^(3/2) - 6578418 z^2 - 2750209 z^(5/2) + 6369363 z^3 + 2081079 z^(7/2) + 315315 z^4 + 945945 z^(9/2) - 3090087 z^5 - 4720911 z^(11/2) + 3166371 z^6 + 4502628 z^(13/2) - 1400256 z^7 - 1916928 z^(15/2) + 239616 z^8 + 319488 z^(17/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)








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