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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=15/4





http://functions.wolfram.com/07.23.03.ag6b.01









  


  










Input Form





Hypergeometric2F1[-(5/4), 15/4, -(9/2), z] == (1/(620928 Pi^(3/2))) (((1/(-1 + z)^7) (2 (-155232 + 905520 z - 2049894 z^2 + 2029181 z^3 - 315315 z^4 - 609609 z^5 + 881205 z^6 - 438048 z^7 + 79872 z^8) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^7) (2 (-155232 + 905520 z - 2049894 z^2 + 2029181 z^3 - 315315 z^4 - 609609 z^5 + 881205 z^6 - 438048 z^7 + 79872 z^8) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^6)) ((155232 - 77616 Sqrt[z] - 827904 z + 381612 z^(3/2) + 1668282 z^2 - 677831 z^(5/2) - 1351350 z^3 + 405405 z^(7/2) - 90090 z^4 + 195195 z^(9/2) + 414414 z^5 - 606957 z^(11/2) - 274248 z^6 + 378144 z^(13/2) + 59904 z^7 - 79872 z^(15/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^7)) ((-155232 - 77616 Sqrt[z] + 827904 z + 381612 z^(3/2) - 1668282 z^2 - 677831 z^(5/2) + 1351350 z^3 + 405405 z^(7/2) + 90090 z^4 + 195195 z^(9/2) - 414414 z^5 - 606957 z^(11/2) + 274248 z^6 + 378144 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