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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.a9t6.01









  


  








Input Form





Hypergeometric2F1[-(19/4), 19/4, 4, -z] == (1/(140821065 Pi z^3)) (256 (1 + z)^(1/4) (2 (608 - 4237 z + 39102 z^2 + 940515 z^3 + 3407304 z^4 + 5018832 z^5 + 3357120 z^6 + 848640 z^7) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - (608 - 4237 z + 39102 z^2 + 940515 z^3 + 3407304 z^4 + 5018832 z^5 + 3357120 z^6 + 848640 z^7) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + Sqrt[1 + z] (-608 + 4693 z - 42693 z^2 + 192246 z^3 + 2580144 z^4 + 6084000 z^5 + 5441280 z^6 + 1697280 z^7) EllipticK[1/2 - 1/(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