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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.aelf.01









  


  








Input Form





Hypergeometric2F1[-(9/4), 19/4, -(11/2), z] == (1/(4553472 Pi^(3/2))) (((1/(-1 + z)^8) (2 (1138368 - 6752592 z + 15156680 z^2 - 14065513 z^3 + 1653652 z^4 + 1611610 z^5 + 5521516 z^6 - 14600105 z^7 + 12947584 z^8 - 5298176 z^9 + 851968 z^10) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^8) (2 (1138368 - 6752592 z + 15156680 z^2 - 14065513 z^3 + 1653652 z^4 + 1611610 z^5 + 5521516 z^6 - 14600105 z^7 + 12947584 z^8 - 5298176 z^9 + 851968 z^10) EllipticE[(1/2) (1 + Sqrt[z])]) - (1/((-1 + Sqrt[z])^8 (1 + Sqrt[z])^7)) ((1138368 - 569184 Sqrt[z] - 6183408 z + 2854544 z^(3/2) + 12302136 z^2 - 4981438 z^(5/2) - 9084075 z^3 + 2557555 z^(7/2) - 903903 z^4 + 1380379 z^(9/2) + 231231 z^5 + 497497 z^(11/2) + 5024019 z^6 - 7943897 z^(13/2) - 6656208 z^7 + 9553024 z^(15/2) + 3394560 z^8 - 4659200 z^(17/2) - 638976 z^9 + 851968 z^(19/2)) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^8)) ((-1138368 - 569184 Sqrt[z] + 6183408 z + 2854544 z^(3/2) - 12302136 z^2 - 4981438 z^(5/2) + 9084075 z^3 + 2557555 z^(7/2) + 903903 z^4 + 1380379 z^(9/2) - 231231 z^5 + 497497 z^(11/2) - 5024019 z^6 - 7943897 z^(13/2) + 6656208 z^7 + 9553024 z^(15/2) - 3394560 z^8 - 4659200 z^(17/2) + 638976 z^9 + 851968 z^(19/2)) 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