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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=-13/8





http://functions.wolfram.com/07.23.03.b9vn.01









  


  










Input Form





Hypergeometric2F1[-(39/8), -(13/8), 2, z] == (16 2^(1/4) (2 Sqrt[1 - z] (46345 + 2671688 z + 5088822 z^2 + 346580 z^3 - 47255 z^4 + 3900 z^5) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (46345 + 2671688 z + 5088822 z^2 + 346580 z^3 - 47255 z^4 + 3900 z^5) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (46345 + 2671688 z + 5088822 z^2 + 346580 z^3 - 47255 z^4 + 3900 z^5) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (46345 - 3075092 z - 18965618 z^2 - 11099140 z^3 + 744185 z^4 - 98800 z^5 + 7800 z^6) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (45742515 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z)










Standard Form





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MathML Form







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<apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 11099140 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 18965618 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3075092 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 46345 </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'> 45742515 </cn> <pi /> <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> 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Rule Form





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





2007-05-02