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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=-9/4, b>=a > For fixed z and a=-9/4, b=19/4





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









  


  








Input Form





Hypergeometric2F1[-(9/4), 19/4, -(9/2), z] == (1/(206976 Pi^(3/2))) (((1/(-1 + z)^7) (2 (-51744 + 232848 z - 326018 z^2 + 54439 z^3 + 63063 z^4 + 249557 z^5 - 781889 z^6 + 795264 z^7 - 366592 z^8 + 65536 z^9) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^7) (2 (-51744 + 232848 z - 326018 z^2 + 54439 z^3 + 63063 z^4 + 249557 z^5 - 781889 z^6 + 795264 z^7 - 366592 z^8 + 65536 z^9) EllipticE[(1/2) (1 + Sqrt[z])]) - (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^6)) ((-51744 + 25872 Sqrt[z] + 206976 z - 92708 z^(3/2) - 233310 z^2 + 78925 z^(5/2) - 24486 z^3 + 42273 z^(7/2) + 20790 z^4 + 8855 z^(9/2) + 240702 z^5 - 392561 z^(11/2) - 389328 z^6 + 564864 z^(13/2) + 230400 z^7 - 317440 z^(15/2) - 49152 z^8 + 65536 z^(17/2)) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^7)) ((51744 + 25872 Sqrt[z] - 206976 z - 92708 z^(3/2) + 233310 z^2 + 78925 z^(5/2) + 24486 z^3 + 42273 z^(7/2) - 20790 z^4 + 8855 z^(9/2) - 240702 z^5 - 392561 z^(11/2) + 389328 z^6 + 564864 z^(13/2) - 230400 z^7 - 317440 z^(15/2) + 49152 z^8 + 65536 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