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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=-31/8, b>=a > For fixed z and a=-31/8, b=-5/8





http://functions.wolfram.com/07.23.03.bey5.01









  


  










Input Form





Hypergeometric2F1[-(31/8), -(5/8), 6, z] == (524288 2^(1/4) (2 Sqrt[1 - z] (23363584 - 278811520 z + 1620303195 z^2 - 6497408575 z^3 + 24967727050 z^4 + 84774544050 z^5 + 4878732495 z^6 - 552589635 z^7 + 37662300 z^8) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (23363584 - 278811520 z + 1620303195 z^2 - 6497408575 z^3 + 24967727050 z^4 + 84774544050 z^5 + 4878732495 z^6 - 552589635 z^7 + 37662300 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (23363584 - 278811520 z + 1620303195 z^2 - 6497408575 z^3 + 24967727050 z^4 + 84774544050 z^5 + 4878732495 z^6 - 552589635 z^7 + 37662300 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (23363584 - 293413760 z + 1792164715 z^2 - 7482631975 z^3 + 28875180950 z^4 - 289516716790 z^5 - 178576841625 z^6 + 10356086325 z^7 - 1146607800 z^8 + 75324600 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (94183744201161615 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^5)










Standard Form





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MathML Form







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<apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 37662300 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 552589635 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4878732495 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 84774544050 </cn> <apply> <power /> <ci> z </ci> <cn 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z </ci> </apply> </apply> <cn type='integer'> 23363584 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 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Rule Form





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





2007-05-02