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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=-39/8, b>=a > For fixed z and a=-39/8, b=11/8





http://functions.wolfram.com/07.23.03.ba6p.01









  


  










Input Form





Hypergeometric2F1[-(39/8), 11/8, 1, z] == (2 2^(1/4) (4 Sqrt[1 - z] (313499 - 1352114 z + 2117271 z^2 - 1453296 z^3 + 371280 z^4) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + 2 Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (313499 - 1352114 z + 2117271 z^2 - 1453296 z^3 + 371280 z^4) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 2 Sqrt[1 - z] (313499 - 1352114 z + 2117271 z^2 - 1453296 z^3 + 371280 z^4) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (346247 - 3473302 z + 9439703 z^2 - 11484408 z^3 + 6630000 z^4 - 1485120 z^5) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (973245 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]])










Standard Form





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MathML Form







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</apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02