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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=13/4





http://functions.wolfram.com/07.23.03.a9nf.01









  


  








Input Form





Hypergeometric2F1[-(19/4), 13/4, 2, -z] == (1/(1514205 Pi z Sqrt[1 + Sqrt[1 + z]])) (8 Sqrt[2] (Sqrt[1 + z] (7315 + 657407 z + 3747904 z^2 + 7390720 z^3 + 6127616 z^4 + 1835008 z^5) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + (7315 + 664722 z + 4405311 z^2 + 11138624 z^3 + 13518336 z^4 + 7962624 z^5 + 1835008 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (7315 + 284342 z + 1294843 z^2 + 2219392 z^3 + 1660928 z^4 + 458752 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (7315 + 657407 z + 3747904 z^2 + 7390720 z^3 + 6127616 z^4 + 1835008 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + 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