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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.b4rd.01









  


  










Input Form





Hypergeometric2F1[-(47/8), -(27/8), 4, z] == (2048 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-3178451328 + 88872478929 z - 1874144027574 z^2 - 94769495602397 z^3 - 324387555205560 z^4 - 262844665395417 z^5 - 47866720763134 z^6 - 96637148091 z^7 + 2821522572 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) (-3178451328 + 88872478929 z - 1874144027574 z^2 - 94769495602397 z^3 - 324387555205560 z^4 - 262844665395417 z^5 - 47866720763134 z^6 - 96637148091 z^7 + 2821522572 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (-3178451328 + 88872478929 z - 1874144027574 z^2 - 94769495602397 z^3 - 324387555205560 z^4 - 262844665395417 z^5 - 47866720763134 z^6 - 96637148091 z^7 + 2821522572 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (-3178451328 + 90064398177 z - 1907145291753 z^2 + 58558847470417 z^3 + 456027763388127 z^4 + 681005505246843 z^5 + 255061393079213 z^6 + 15048825764643 z^7 - 391956510627 z^8 + 11286090288 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (156297706312272525 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