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





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









  


  








Input Form





Hypergeometric2F1[-(11/4), 11/2, 5, z] == (128 Sqrt[2] (2 (1 - z)^(1/4) (-2816 - 10560 z - 38412 z^2 - 204952 z^3 + 2920515 z^4 - 5071950 z^5 + 2403375 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-2816 - 10560 z - 38412 z^2 - 204952 z^3 + 2920515 z^4 - 5071950 z^5 + 2403375 z^6) EllipticE[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (-2816 - 10560 z - 38412 z^2 - 204952 z^3 + 2920515 z^4 - 5071950 z^5 + 2403375 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (-2816 - 10560 z - 38412 z^2 - 204952 z^3 + 2920515 z^4 - 5071950 z^5 + 2403375 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (-2816 - 10560 z - 38412 z^2 - 204952 z^3 + 2920515 z^4 - 5071950 z^5 + 2403375 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (-2816 - 9152 z - 32868 z^2 - 184624 z^3 - 166855 z^4 + 3550365 z^5 - 5552625 z^6 + 2403375 z^7) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (204417675 Pi Sqrt[1 + Sqrt[1 - z]] z^4)








Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2007-05-02