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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=-19/4, b>=a > For fixed z and a=-19/4, b=19/4





http://functions.wolfram.com/07.23.03.a9t0.01









  


  








Input Form





Hypergeometric2F1[-(19/4), 19/4, 3, z] == (1/(13627845 Pi z^2)) (64 Sqrt[1 + Sqrt[z]] ((-532 - 9975 z + 400611 z^2 - 1951752 z^3 + 3596112 z^4 - 2882880 z^5 + 848640 z^6) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - 2 (-266 + 266 Sqrt[z] - 5187 z + 5187 z^(3/2) - 16551 z^2 + 16551 z^(5/2) + 599232 z^3 - 599232 z^(7/2) - 1974960 z^4 + 1974960 z^(9/2) + 2246400 z^5 - 2246400 z^(11/2) - 848640 z^6 + 848640 z^(13/2)) 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