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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=-25/8, b>=a > For fixed z and a=-25/8, b=37/8





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









  


  










Input Form





Hypergeometric2F1[-(25/8), 37/8, 3, z] == (1/(13657418775 Pi z^2)) (128 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-16 (33150 + 447525 z - 36828438 z^2 + 154082324 z^3 - 205124304 z^4 + 87218208 z^5) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (16575 - 21113235 z + 96102456 z^2 - 133288496 z^3 + 58145472 z^4) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-16575 - 35802000 z + 173473344 z^2 - 254117248 z^3 + 116290944 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 8 (33150 + 447525 z - 36828438 z^2 + 154082324 z^3 - 205124304 z^4 + 87218208 z^5) EllipticK[1/2 - 1/(Sqrt[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