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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=47/8





http://functions.wolfram.com/07.23.03.b8ce.01









  


  










Input Form





Hypergeometric2F1[-(43/8), 47/8, 6, z] == (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (2650374144 + 6139343232 z + 17952386265 z^2 + 71681021973 z^3 + 508967358471 z^4 - 14828539830945 z^5 + 59220323696540 z^6 - 103886448268400 z^7 + 94432835228160 z^8 - 43762079412480 z^9 + 8213528294400 z^10) EllipticE[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-331296768 - 1008125712 z - 2999869587 z^2 - 11222192718 z^3 - 8446613712075 z^4 + 42081199936140 z^5 - 83632777977040 z^6 + 83097498415360 z^7 - 41298020924160 z^8 + 8213528294400 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 20 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-82824192 - 205442820 z - 598857732 z^2 - 2350702629 z^3 + 1239860359980 z^4 - 6837745055685 z^5 + 15896080502150 z^6 - 19815219045440 z^7 + 13937686139520 z^8 - 5238628412160 z^9 + 821352829440 z^10) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (2650374144 + 6139343232 z + 17952386265 z^2 + 71681021973 z^3 + 508967358471 z^4 - 14828539830945 z^5 + 59220323696540 z^6 - 103886448268400 z^7 + 94432835228160 z^8 - 43762079412480 z^9 + 8213528294400 z^10) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/(6586042357551732075 Pi 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