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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=-21/8, b>=a > For fixed z and a=-21/8, b=-17/8





http://functions.wolfram.com/07.23.03.bl69.01









  


  










Input Form





Hypergeometric2F1[-(21/8), -(17/8), 4, z] == (2048 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (198016 - 2838745 z + 27010620 z^2 + 1042706930 z^3 + 1171132300 z^4 + 165137055 z^5) EllipticE[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[1 - z] (198016 - 2838745 z + 27010620 z^2 + 1042706930 z^3 + 1171132300 z^4 + 165137055 z^5) EllipticK[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (198016 - 2838745 z + 27010620 z^2 + 1042706930 z^3 + 1171132300 z^4 + 165137055 z^5) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (-198016 + 2913001 z - 28054845 z^2 - 210389990 z^3 + 99590150 z^4 + 130274445 z^5 + 5865255 z^6) EllipticK[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (842207491125 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4) z^3)










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