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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=13/8





http://functions.wolfram.com/07.23.03.b586.01









  


  










Input Form





Hypergeometric2F1[-(47/8), 13/8, 5, z] == (65536 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-1338295296 + 10023274144 z - 28768556791 z^2 + 22944445524 z^3 - 68316756706 z^4 + 90172224868 z^5 - 70904834847 z^6 + 34054366368 z^7 - 9271333632 z^8 + 1101754368 z^9) 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) (-1338295296 + 10023274144 z - 28768556791 z^2 + 22944445524 z^3 - 68316756706 z^4 + 90172224868 z^5 - 70904834847 z^6 + 34054366368 z^7 - 9271333632 z^8 + 1101754368 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (-1338295296 + 10023274144 z - 28768556791 z^2 + 22944445524 z^3 - 68316756706 z^4 + 90172224868 z^5 - 70904834847 z^6 + 34054366368 z^7 - 9271333632 z^8 + 1101754368 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-669147648 + 5262567440 z - 16195028525 z^2 + 16388889660 z^3 + 97772183410 z^4 - 210984716668 z^5 + 241953622515 z^6 - 172589098440 z^7 + 76759446720 z^8 - 19598515200 z^9 + 2203508736 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (8847808402407975 Pi (1 + Sqrt[1 - z])^(1/4) z^4)










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