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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=-9/2, b>=a > For fixed z and a=-9/2, b=15/4





http://functions.wolfram.com/07.23.03.aa4n.01









  


  








Input Form





Hypergeometric2F1[-(9/2), 15/4, 3, z] == (2 (-5760 - 66240 z + 2143408 z^2 - 8495104 z^3 + 13233480 z^4 - 9215700 z^5 + 2403375 z^6) EllipticE[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-5760 - 66240 z + 2143408 z^2 - 8495104 z^3 + 13233480 z^4 - 9215700 z^5 + 2403375 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (5760 + 66240 z - 2143408 z^2 + 8495104 z^3 - 13233480 z^4 + 9215700 z^5 - 2403375 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (5760 + 66240 z - 2143408 z^2 + 8495104 z^3 - 13233480 z^4 + 9215700 z^5 - 2403375 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (5760 + 66240 z - 2143408 z^2 + 8495104 z^3 - 13233480 z^4 + 9215700 z^5 - 2403375 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (5760 + 69120 z - 125968 z^2 - 2457520 z^3 + 7399080 z^4 - 7293000 z^5 + 2403375 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (495495 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z^2)








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