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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=11/4





http://functions.wolfram.com/07.23.03.a81s.01









  


  








Input Form





Hypergeometric2F1[-(11/2), 11/4, 5, z] == (4 Sqrt[2] (-2 (811008 - 3108864 z + 1351680 z^2 + 3252480 z^3 - 32131840 z^4 + 71072864 z^5 - 79314112 z^6 + 49778040 z^7 - 16840200 z^8 + 2403375 z^9) EllipticE[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (811008 - 3108864 z + 1351680 z^2 + 3252480 z^3 - 32131840 z^4 + 71072864 z^5 - 79314112 z^6 + 49778040 z^7 - 16840200 z^8 + 2403375 z^9) EllipticE[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (811008 - 3108864 z + 1351680 z^2 + 3252480 z^3 - 32131840 z^4 + 71072864 z^5 - 79314112 z^6 + 49778040 z^7 - 16840200 z^8 + 2403375 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (811008 - 3108864 z + 1351680 z^2 + 3252480 z^3 - 32131840 z^4 + 71072864 z^5 - 79314112 z^6 + 49778040 z^7 - 16840200 z^8 + 2403375 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (811008 - 3108864 z + 1351680 z^2 + 3252480 z^3 - 32131840 z^4 + 71072864 z^5 - 79314112 z^6 + 49778040 z^7 - 16840200 z^8 + 2403375 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (-811008 + 2703360 z - 126720 z^2 - 2956800 z^3 - 5567360 z^4 + 31257696 z^5 - 48920560 z^6 + 37844040 z^7 - 14917500 z^8 + 2403375 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (72747675 Pi Sqrt[1 + Sqrt[1 - z]] z^4)








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