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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=-13/4, b>=a > For fixed z and a=-13/4, b=1/4





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









  


  








Input Form





Hypergeometric2F1[-(13/4), 1/4, 6, z] == -((1/(487336674825 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((-79872 + 767520 z - 3407157 z^2 + 9566700 z^3 - 21737430 z^4 - 52158876 z^5 + 10014235 z^6 - 1860936 z^7 + 175560 z^8) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (79872 - 79872 Sqrt[z] - 707616 z + 707616 z^(3/2) + 2885805 z^2 - 2885805 z^(5/2) - 7481760 z^3 + 7481760 z^(7/2) + 16434990 z^4 - 16434990 z^(9/2) + 4230996 z^5 - 4230996 z^(11/2) - 850003 z^6 + 850003 z^(13/2) + 87780 z^7 - 87780 z^(15/2)) EllipticK[(2 Sqrt[z])/(1 + Sqrt[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