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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=-23/4, b>=a > For fixed z and a=-23/4, b=17/4





http://functions.wolfram.com/07.23.03.9992.01









  


  










Input Form





Hypergeometric2F1[-(23/4), 17/4, 21/4, z] == (1/(676457349120 z^(17/4))) (17 (-8 (1 - z)^(3/4) z^(1/4) (19684665 + 15747732 z + 13997984 z^2 + 12921216 z^3 - 4961789952 z^4 + 19433676800 z^5 - 32077971456 z^6 + 27343454208 z^7 - 11920211968 z^8 + 2113929216 z^9) - 39369330 Sqrt[2] ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 39369330 Sqrt[2] ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 19684665 Sqrt[2] Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 19684665 Sqrt[2] Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - 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