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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=-17/4, b>=a > For fixed z and a=-17/4, b=19/4





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









  


  








Input Form





Hypergeometric2F1[-(17/4), 19/4, -(11/2), z] == (1/(40981248 Pi^(3/2))) (((1/(-1 + z)^6) (2 (10245312 - 22586256 z + 3816120 z^2 + 3276735 z^3 + 4726799 z^4 + 11066517 z^5 + 70520373 z^6 - 339840640 z^7 + 465745920 z^8 - 271122432 z^9 + 58720256 z^10) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^6) (2 (10245312 - 22586256 z + 3816120 z^2 + 3276735 z^3 + 4726799 z^4 + 11066517 z^5 + 70520373 z^6 - 339840640 z^7 + 465745920 z^8 - 271122432 z^9 + 58720256 z^10) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^5)) ((-10245312 + 5122656 Sqrt[z] + 17463600 z - 6597360 z^(3/2) + 2781240 z^2 - 3961650 z^(5/2) + 684915 z^3 - 2150225 z^(7/2) - 2576574 z^4 + 201432 z^(9/2) - 11267949 z^5 + 5561787 z^(11/2) - 76082160 z^6 + 137134720 z^(13/2) + 202705920 z^7 - 302315520 z^(15/2) - 163430400 z^8 + 227082240 z^(17/2) + 44040192 z^9 - 58720256 z^(19/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^6)) ((10245312 + 5122656 Sqrt[z] - 17463600 z - 6597360 z^(3/2) - 2781240 z^2 - 3961650 z^(5/2) - 684915 z^3 - 2150225 z^(7/2) + 2576574 z^4 + 201432 z^(9/2) + 11267949 z^5 + 5561787 z^(11/2) + 76082160 z^6 + 137134720 z^(13/2) - 202705920 z^7 - 302315520 z^(15/2) + 163430400 z^8 + 227082240 z^(17/2) - 44040192 z^9 - 58720256 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