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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=-1/4





http://functions.wolfram.com/07.23.03.a7z7.01









  


  










Input Form





Hypergeometric2F1[-(11/2), -(1/4), 2, z] == (2 (44352 + 2440288 z + 392992 z^2 - 229088 z^3 + 100932 z^4 - 27222 z^5 + 3315 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (44352 + 2440288 z + 392992 z^2 - 229088 z^3 + 100932 z^4 - 27222 z^5 + 3315 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (44352 + 2440288 z + 392992 z^2 - 229088 z^3 + 100932 z^4 - 27222 z^5 + 3315 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (44352 + 2440288 z + 392992 z^2 - 229088 z^3 + 100932 z^4 - 27222 z^5 + 3315 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (44352 + 2440288 z + 392992 z^2 - 229088 z^3 + 100932 z^4 - 27222 z^5 + 3315 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (-44352 - 1021024 z + 260736 z^2 - 163904 z^3 + 81276 z^4 - 24570 z^5 + 3315 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (360360 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