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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=15/4





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









  


  








Input Form





Hypergeometric2F1[-(1/4), 15/4, -(11/2), z] == (1/(1951488 Pi^(3/2))) (((1/(-1 + z)^9) (2 (-487872 + 4246704 z - 16275336 z^2 + 35820939 z^3 - 49170924 z^4 + 41563346 z^5 - 12864852 z^6 + 7413003 z^7 - 2110992 z^8 + 254592 z^9) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^9) (2 (-487872 + 4246704 z - 16275336 z^2 + 35820939 z^3 - 49170924 z^4 + 41563346 z^5 - 12864852 z^6 + 7413003 z^7 - 2110992 z^8 + 254592 z^9) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^9 (1 + Sqrt[z])^8)) ((487872 - 243936 Sqrt[z] - 4002768 z + 1899744 z^(3/2) + 14375592 z^2 - 6404706 z^(5/2) - 29416233 z^3 + 12102024 z^(7/2) + 37068900 z^4 - 13689500 z^(9/2) - 27873846 z^5 + 8576568 z^(11/2) + 4288284 z^6 - 6002802 z^(13/2) - 1410201 z^7 + 1920048 z^(15/2) + 190944 z^8 - 254592 z^(17/2)) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^8 (1 + Sqrt[z])^9)) ((487872 + 243936 Sqrt[z] - 4002768 z - 1899744 z^(3/2) + 14375592 z^2 + 6404706 z^(5/2) - 29416233 z^3 - 12102024 z^(7/2) + 37068900 z^4 + 13689500 z^(9/2) - 27873846 z^5 - 8576568 z^(11/2) + 4288284 z^6 + 6002802 z^(13/2) - 1410201 z^7 - 1920048 z^(15/2) + 190944 z^8 + 254592 z^(17/2)) 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