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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.a7xu.01









  


  








Input Form





Hypergeometric2F1[-(11/2), -(9/4), 3, z] == (2 (-19712 + 625856 z + 49857856 z^2 + 154638688 z^3 + 79026352 z^4 + 699244 z^5 - 60112 z^6 + 3315 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-19712 + 625856 z + 49857856 z^2 + 154638688 z^3 + 79026352 z^4 + 699244 z^5 - 60112 z^6 + 3315 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (-19712 + 625856 z + 49857856 z^2 + 154638688 z^3 + 79026352 z^4 + 699244 z^5 - 60112 z^6 + 3315 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (-19712 + 625856 z + 49857856 z^2 + 154638688 z^3 + 79026352 z^4 + 699244 z^5 - 60112 z^6 + 3315 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (-19712 + 625856 z + 49857856 z^2 + 154638688 z^3 + 79026352 z^4 + 699244 z^5 - 60112 z^6 + 3315 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (19712 - 616000 z - 23616256 z^2 - 53718816 z^3 - 17591600 z^4 + 653276 z^5 - 57460 z^6 + 3315 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (6636630 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