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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=-11/4, b>=a > For fixed z and a=-11/4, b=-5/2





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









  


  








Input Form





Hypergeometric2F1[-(11/4), -(5/2), 6, z] == (64 Sqrt[2] (2 (1 - z)^(1/4) (16384 - 231936 z + 1655712 z^2 - 8578960 z^3 + 45981000 z^4 + 409239576 z^5 + 258928386 z^6 + 22173813 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (16384 - 231936 z + 1655712 z^2 - 8578960 z^3 + 45981000 z^4 + 409239576 z^5 + 258928386 z^6 + 22173813 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (16384 - 231936 z + 1655712 z^2 - 8578960 z^3 + 45981000 z^4 + 409239576 z^5 + 258928386 z^6 + 22173813 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (16384 - 231936 z + 1655712 z^2 - 8578960 z^3 + 45981000 z^4 + 409239576 z^5 + 258928386 z^6 + 22173813 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (16384 - 231936 z + 1655712 z^2 - 8578960 z^3 + 45981000 z^4 + 409239576 z^5 + 258928386 z^6 + 22173813 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-16384 + 240128 z - 1770144 z^2 + 9385840 z^3 - 50125640 z^4 + 127894704 z^5 + 475248342 z^6 + 162336729 z^7 + 5990400 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (16476064605 Pi Sqrt[1 + Sqrt[1 - z]] z^5)








Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2007-05-02