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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=3/2





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









  


  








Input Form





Hypergeometric2F1[-(11/4), 3/2, 4, z] == (1/(504735 Pi Sqrt[1 + Sqrt[1 - z]] z^3)) (64 Sqrt[2] (2 (1 - z)^(1/4) (-1232 + 4851 z - 4620 z^2 + 8312 z^3 - 5166 z^4 + 1170 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] + 2 (1 - z)^(3/4) (-1232 + 4851 z - 4620 z^2 + 8312 z^3 - 5166 z^4 + 1170 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] - (1 - z)^(1/4) (-1232 + 4851 z - 4620 z^2 + 8312 z^3 - 5166 z^4 + 1170 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] - Sqrt[1 - z] (-1232 + 4851 z - 4620 z^2 + 8312 z^3 - 5166 z^4 + 1170 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] - (1 - z)^(3/4) (-1232 + 4851 z - 4620 z^2 + 8312 z^3 - 5166 z^4 + 1170 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] - (-1232 + 5467 z - 6930 z^2 - 5548 z^3 + 9158 z^4 - 5400 z^5 + 1170 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 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