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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 3 and fixed z > For fixed z and a=-8/3, b>=a > For fixed z and a=-8/3, b=-4/3





http://functions.wolfram.com/07.23.03.6168.01









  


  










Input Form





Hypergeometric2F1[-(8/3), -(4/3), 11/2, -z] == (6561 (Sqrt[z] (-165888 - 2039808 z - 12486656 z^2 - 55889920 z^3 + 834250195 z^4 + 505489831 z^5 - 372041884 z^6 + 1995664 z^7) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[1 + z] (497664 + 5971968 z + 35756032 z^2 + 157822976 z^3 + 928657408 z^4 - 2475135473 z^5 + 601543244 z^6 + 1995664 z^7) Sinh[ArcSinh[Sqrt[z]]/3]))/ (7597422376115 z^(9/2) 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