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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 8 and fixed z and a<0 > For fixed z and a=-19/8, b>=a > For fixed z and a=-19/8, b=39/8





http://functions.wolfram.com/07.23.03.bn0w.01









  


  










Input Form





Hypergeometric2F1[-(19/8), 39/8, 3, z] == (1/(140821065 Pi z^2)) (128 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-1672 - 21109 z + 631176 z^2 - 1644240 z^3 + 1060800 z^4) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (209 + 369512 z - 1326000 z^2 + 1060800 z^3) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (209 - 217360 z + 891072 z^2 - 1103232 z^3 + 424320 z^4) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (-1672 - 21109 z + 631176 z^2 - 1644240 z^3 + 1060800 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))










Standard Form





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MathML Form







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</math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02