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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=-47/8, b>=a > For fixed z and a=-47/8, b=-45/8





http://functions.wolfram.com/07.23.03.b4ld.01









  


  










Input Form





Hypergeometric2F1[-(47/8), -(45/8), 6, z] == (524288 2^(1/4) (2 Sqrt[1 - z] (22964371456 - 650806698880 z + 10155255316115 z^2 - 128586547911640 z^3 + 1943382823147220 z^4 + 67785684724869272 z^5 + 244478689039911410 z^6 + 270621452224626200 z^7 + 104608268011375700 z^8 + 12847250602786600 z^9 + 329297289948627 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (22964371456 - 650806698880 z + 10155255316115 z^2 - 128586547911640 z^3 + 1943382823147220 z^4 + 67785684724869272 z^5 + 244478689039911410 z^6 + 270621452224626200 z^7 + 104608268011375700 z^8 + 12847250602786600 z^9 + 329297289948627 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (22964371456 - 650806698880 z + 10155255316115 z^2 - 128586547911640 z^3 + 1943382823147220 z^4 + 67785684724869272 z^5 + 244478689039911410 z^6 + 270621452224626200 z^7 + 104608268011375700 z^8 + 12847250602786600 z^9 + 329297289948627 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (-22964371456 + 665159431040 z - 10559654757795 z^2 + 134867953162215 z^3 - 2022738714835020 z^4 + 80080566776475468 z^5 + 599005604525857830 z^6 + 1149970544964017730 z^7 + 779234842593257700 z^8 + 189525655305629500 z^9 + 13896622233026533 z^10 + 163814150074575 z^11) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (38447180109570921543855 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^5)










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