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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=-23/4, b>=a > For fixed z and a=-23/4, b=-23/4





http://functions.wolfram.com/07.23.03.8953.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(23/4), 3, -z] == (64 Sqrt[2] (-2 Sqrt[1 + z] (336490 + 20021155 z - 2008984896 z^2 + 14446123217 z^3 - 27667651582 z^4 + 16861945797 z^5 - 3045132812 z^6 + 107661031 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 2 (336490 + 20357645 z - 1988963741 z^2 + 12437138321 z^3 - 13221528365 z^4 - 10805705785 z^5 + 13816812985 z^6 - 2937471781 z^7 + 107661031 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 2 Sqrt[1 + z] (336490 + 20021155 z - 2008984896 z^2 + 14446123217 z^3 - 27667651582 z^4 + 16861945797 z^5 - 3045132812 z^6 + 107661031 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (672980 + 40547045 z - 304634397 z^2 - 14487412535 z^3 + 78491665015 z^4 - 109242400305 z^5 + 48398238665 z^6 - 6212706877 z^7 + 140821065 z^8) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (117867231405 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