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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=-3/4, b>=a > For fixed z and a=-3/4, b=17/4





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









  


  










Input Form





Hypergeometric2F1[-(3/4), 17/4, -(9/2), z] == (1/(18720 Pi^(3/2))) (((1/(-1 + z)^8) (2 Sqrt[z] (9360 - 64740 z + 184353 z^2 - 263484 z^3 + 150150 z^4 - 582120 z^5 + 437745 z^6 - 155936 z^7 + 22528 z^8) EllipticE[(1/2) (1 - Sqrt[z])]) - (1/(-1 + z)^8) (2 Sqrt[z] (9360 - 64740 z + 184353 z^2 - 263484 z^3 + 150150 z^4 - 582120 z^5 + 437745 z^6 - 155936 z^7 + 22528 z^8) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^8 (1 + Sqrt[z])^7)) ((18720 - 28080 Sqrt[z] - 115440 z + 180180 z^(3/2) + 283530 z^2 - 467883 z^(5/2) - 322101 z^3 + 585585 z^(7/2) + 75075 z^4 - 225225 z^(9/2) + 345345 z^5 + 236775 z^(11/2) - 336105 z^6 - 101640 z^(13/2) + 139040 z^7 + 16896 z^(15/2) - 22528 z^8) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^8)) ((-18720 - 28080 Sqrt[z] + 115440 z + 180180 z^(3/2) - 283530 z^2 - 467883 z^(5/2) + 322101 z^3 + 585585 z^(7/2) - 75075 z^4 - 225225 z^(9/2) - 345345 z^5 + 236775 z^(11/2) + 336105 z^6 - 101640 z^(13/2) - 139040 z^7 + 16896 z^(15/2) + 22528 z^8) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^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