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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.a818.01









  


  










Input Form





Hypergeometric2F1[-(11/2), 9/4, 2, z] == (-2 (1 - z)^(1/4) (44352 - 2706400 z + 13259712 z^2 - 26632800 z^3 + 26839780 z^4 - 13526898 z^5 + 2725569 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (44352 - 2706400 z + 13259712 z^2 - 26632800 z^3 + 26839780 z^4 - 13526898 z^5 + 2725569 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (44352 - 1287136 z + 5509664 z^2 - 10218240 z^3 + 9721540 z^4 - 4682018 z^5 + 908523 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (44352 - 2706400 z + 13259712 z^2 - 26632800 z^3 + 26839780 z^4 - 13526898 z^5 + 2725569 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (44352 - 2706400 z + 13259712 z^2 - 26632800 z^3 + 26839780 z^4 - 13526898 z^5 + 2725569 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (44352 - 2706400 z + 13259712 z^2 - 26632800 z^3 + 26839780 z^4 - 13526898 z^5 + 2725569 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 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