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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=-23/4





http://functions.wolfram.com/07.23.03.8946.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(23/4), 5/4, z] == (1/171798691840) (24 (1 - z)^(3/4) (5271186825 + 102615094404 z + 375202787840 z^2 + 371694852096 z^3 + 99487644672 z^4 + 4933726208 z^5) - (1/z^(1/4)) (336490 Sqrt[2] (33649 + 1615152 z + 11536800 z^2 + 22374400 z^3 + 13424640 z^4 + 2260992 z^5 + 65536 z^6) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) - (1/z^(1/4)) (336490 Sqrt[2] (33649 + 1615152 z + 11536800 z^2 + 22374400 z^3 + 13424640 z^4 + 2260992 z^5 + 65536 z^6) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) - (1/z^(1/4)) (168245 Sqrt[2] (33649 + 1615152 z + 11536800 z^2 + 22374400 z^3 + 13424640 z^4 + 2260992 z^5 + 65536 z^6) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]) + (1/z^(1/4)) (168245 Sqrt[2] (33649 + 1615152 z + 11536800 z^2 + 22374400 z^3 + 13424640 z^4 + 2260992 z^5 + 65536 z^6) 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