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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=-1/4, b>=a > For fixed z and a=-1/4, b=19/4





http://functions.wolfram.com/07.23.03.aht2.01









  


  










Input Form





Hypergeometric2F1[-(1/4), 19/4, -(7/2), z] == (1/(517440 Pi^(3/2))) (((1/(-1 + z)^8) (2 (129360 - 974820 z + 3117653 z^2 - 5267724 z^3 + 3153150 z^4 - 3414840 z^5 + 1945125 z^6 - 602784 z^7 + 79872 z^8) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^8) (2 (129360 - 974820 z + 3117653 z^2 - 5267724 z^3 + 3153150 z^4 - 3414840 z^5 + 1945125 z^6 - 602784 z^7 + 79872 z^8) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^8 (1 + Sqrt[z])^7)) ((-129360 + 64680 Sqrt[z] + 910140 z - 428120 z^(3/2) - 2689533 z^2 + 1168629 z^(5/2) + 4099095 z^3 - 1576575 z^(7/2) - 1576575 z^4 + 2314455 z^(9/2) + 1100385 z^5 - 1547325 z^(11/2) - 397800 z^6 + 542880 z^(13/2) + 59904 z^7 - 79872 z^(15/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^8)) ((129360 + 64680 Sqrt[z] - 910140 z - 428120 z^(3/2) + 2689533 z^2 + 1168629 z^(5/2) - 4099095 z^3 - 1576575 z^(7/2) + 1576575 z^4 + 2314455 z^(9/2) - 1100385 z^5 - 1547325 z^(11/2) + 397800 z^6 + 542880 z^(13/2) - 59904 z^7 - 79872 z^(15/2)) 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