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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=-21/4





http://functions.wolfram.com/07.23.03.a7w5.01









  


  










Input Form





Hypergeometric2F1[-(11/2), -(21/4), 2, z] == (2 (251328 + 89210656 z + 1017587840 z^2 + 2673023520 z^3 + 2071775820 z^4 + 453737886 z^5 + 18843447 z^6) EllipticE[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (251328 + 89210656 z + 1017587840 z^2 + 2673023520 z^3 + 2071775820 z^4 + 453737886 z^5 + 18843447 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (251328 + 48495520 z + 447130720 z^2 + 948932640 z^3 + 572308140 z^4 + 89052726 z^5 + 1972425 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (251328 + 89210656 z + 1017587840 z^2 + 2673023520 z^3 + 2071775820 z^4 + 453737886 z^5 + 18843447 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (251328 + 89210656 z + 1017587840 z^2 + 2673023520 z^3 + 2071775820 z^4 + 453737886 z^5 + 18843447 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (251328 + 89210656 z + 1017587840 z^2 + 2673023520 z^3 + 2071775820 z^4 + 453737886 z^5 + 18843447 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (10210200 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z)










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