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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=-19/8





http://functions.wolfram.com/07.23.03.b4u4.01









  


  










Input Form





Hypergeometric2F1[-(47/8), -(19/8), 4, z] == (2048 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (1059483776 - 24922700387 z + 427253387106 z^2 + 15757158153835 z^3 + 36074023094060 z^4 + 14879515024899 z^5 + 94643948322 z^6 - 7504082091 z^7 + 368826480 z^8) EllipticE[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (1059483776 - 24922700387 z + 427253387106 z^2 + 15757158153835 z^3 + 36074023094060 z^4 + 14879515024899 z^5 + 94643948322 z^6 - 7504082091 z^7 + 368826480 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (1059483776 - 24922700387 z + 427253387106 z^2 + 15757158153835 z^3 + 36074023094060 z^4 + 14879515024899 z^5 + 94643948322 z^6 - 7504082091 z^7 + 368826480 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (1059483776 - 25320006803 z + 436490761278 z^2 - 11336060292641 z^3 - 61731652437700 z^4 - 55130135479461 z^5 - 6981126098562 z^6 + 392801737977 z^7 - 30723245784 z^8 + 1475305920 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (27581948172753975 Pi (1 + Sqrt[1 - z])^(1/4) z^3)










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