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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=-13/4, b>=a > For fixed z and a=-13/4, b=-1/2





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









  


  








Input Form





Hypergeometric2F1[-(13/4), -(1/2), 4, z] == (16 Sqrt[2] (2 (2496 - 26988 z + 175890 z^2 + 2198075 z^3 + 425600 z^4 - 54208 z^5 + 4704 z^6) EllipticE[1/2 - (1 - z)^(1/4)/ (1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (2496 - 26988 z + 175890 z^2 + 2198075 z^3 + 425600 z^4 - 54208 z^5 + 4704 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (-2496 + 25740 z - 163410 z^2 - 753125 z^3 - 16800 z^4 + 1568 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (2496 - 26988 z + 175890 z^2 + 2198075 z^3 + 425600 z^4 - 54208 z^5 + 4704 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (2496 - 26988 z + 175890 z^2 + 2198075 z^3 + 425600 z^4 - 54208 z^5 + 4704 z^6) EllipticK[1/2 - (1 - z)^(1/4)/ (1 + Sqrt[1 - z])] - Sqrt[1 - z] (2496 - 26988 z + 175890 z^2 + 2198075 z^3 + 425600 z^4 - 54208 z^5 + 4704 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (12182625 Pi Sqrt[1 + Sqrt[1 - z]] z^3)








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