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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=21/4





http://functions.wolfram.com/07.23.03.acv6.01









  


  










Input Form





Hypergeometric2F1[-(13/4), 21/4, 5, z] == (1/(858004875 Pi Sqrt[1 + Sqrt[z]] z^4)) (4096 ((-(384 + 384 Sqrt[z] + 1232 z + 1232 z^(3/2) + 4335 z^2 + 4335 z^(5/2) + 24105 z^3 + 24105 z^(7/2) - 964600 z^4 - 964600 z^(9/2) + 2723952 z^5 + 2723952 z^(11/2) - 2675904 z^6 - 2675904 z^(13/2) + 887040 z^7 + 887040 z^(15/2))) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + 8 (48 + 142 z + 500 z^2 + 2865 z^3 - 69005 z^4 + 181874 z^5 - 171864 z^6 + 55440 z^7) 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