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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=-43/8, b>=a > For fixed z and a=-43/8, b=23/8





http://functions.wolfram.com/07.23.03.b7z0.01









  


  










Input Form





Hypergeometric2F1[-(43/8), 23/8, 6, z] == (1/(12079266380232975 Pi z^5)) (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (-883458048 + 4827960192 z - 8347206483 z^2 + 1171509372 z^3 + 2367768942 z^4 - 22490105460 z^5 + 44529861965 z^6 - 44757614960 z^7 + 25542791040 z^8 - 7927570560 z^9 + 1045948800 z^10) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 24 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (13804032 - 65407386 z + 83875671 z^2 + 38500308 z^3 - 1925015400 z^4 + 4427026440 z^5 - 4829668295 z^6 + 2924110670 z^7 - 951723240 z^8 + 130743600 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (110432256 - 585377232 z + 952882623 z^2 - 16500132 z^3 + 8951321610 z^4 - 25991779740 z^5 + 35526162335 z^6 - 28266616040 z^7 + 13495444560 z^8 - 3610326720 z^9 + 418379520 z^10) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-883458048 + 4827960192 z - 8347206483 z^2 + 1171509372 z^3 + 2367768942 z^4 - 22490105460 z^5 + 44529861965 z^6 - 44757614960 z^7 + 25542791040 z^8 - 7927570560 z^9 + 1045948800 z^10) 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