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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=27/8





http://functions.wolfram.com/07.23.03.b5g1.01









  


  










Input Form





Hypergeometric2F1[-(47/8), 27/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[1 - z] (1098088448 - 4250803328 z + 2794649845 z^2 + 3859796980 z^3 + 9727908190 z^4 - 96696738004 z^5 + 213043615269 z^6 - 234920435720 z^7 + 145148468400 z^8 - 48267460800 z^9 + 6767904000 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (1098088448 - 4250803328 z + 2794649845 z^2 + 3859796980 z^3 + 9727908190 z^4 - 96696738004 z^5 + 213043615269 z^6 - 234920435720 z^7 + 145148468400 z^8 - 48267460800 z^9 + 6767904000 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (1098088448 - 4250803328 z + 2794649845 z^2 + 3859796980 z^3 + 9727908190 z^4 - 96696738004 z^5 + 213043615269 z^6 - 234920435720 z^7 + 145148468400 z^8 - 48267460800 z^9 + 6767904000 z^10) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (1098088448 - 4937108608 z + 5338804965 z^2 + 2496234390 z^3 + 7201178790 z^4 + 92555294056 z^5 - 383817992771 z^6 + 654013035850 z^7 - 618456707440 z^8 + 341733007200 z^9 - 103979616000 z^10 + 13535808000 z^11) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (51317288733966255 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