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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=-11/2, b>=a > For fixed z and a=-11/2, b=-9/4





http://functions.wolfram.com/07.23.03.a7xv.01









  


  








Input Form





Hypergeometric2F1[-(11/2), -(9/4), 4, z] == (2 (22528 - 499840 z + 7949568 z^2 + 405302976 z^3 + 946233504 z^4 + 387747288 z^5 + 2749240 z^6 - 204646 z^7 + 9945 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (22528 - 499840 z + 7949568 z^2 + 405302976 z^3 + 946233504 z^4 + 387747288 z^5 + 2749240 z^6 - 204646 z^7 + 9945 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (22528 - 499840 z + 7949568 z^2 + 405302976 z^3 + 946233504 z^4 + 387747288 z^5 + 2749240 z^6 - 204646 z^7 + 9945 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (22528 - 499840 z + 7949568 z^2 + 405302976 z^3 + 946233504 z^4 + 387747288 z^5 + 2749240 z^6 - 204646 z^7 + 9945 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (22528 - 499840 z + 7949568 z^2 + 405302976 z^3 + 946233504 z^4 + 387747288 z^5 + 2749240 z^6 - 204646 z^7 + 9945 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (-22528 + 488576 z - 7708800 z^2 - 183437376 z^3 - 312823392 z^4 - 82005144 z^5 + 2591888 z^6 - 196690 z^7 + 9945 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (56411355 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z^3)








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