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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=-7/4





http://functions.wolfram.com/07.23.03.a97p.01









  


  










Input Form





Hypergeometric2F1[-(19/4), -(7/4), 3, -z] == (64 Sqrt[2] (Sqrt[1 + z] (-532 - 13167 z + 342756 z^2 - 459698 z^3 + 36792 z^4 + 3465 z^5 + 224 z^6) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + (-532 - 13699 z + 329589 z^2 - 116942 z^3 - 422906 z^4 + 40257 z^5 + 3689 z^6 + 224 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 2 (-266 - 6783 z - 46476 z^2 + 475838 z^3 - 332430 z^4 + 441 z^5 + 28 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-532 - 13167 z + 342756 z^2 - 459698 z^3 + 36792 z^4 + 3465 z^5 + 224 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (13627845 Pi z^2 Sqrt[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