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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 4 and fixed z > For fixed z and a=-23/4, b>=a > For fixed z and a=-23/4, b=1/2





http://functions.wolfram.com/07.23.03.9498.01









  


  








Input Form





Hypergeometric2F1[-(23/4), 1/2, 3, z] == (16 Sqrt[2] (-2 (1 - z)^(1/4) (672980 - 7571025 z - 21508416 z^2 + 21968296 z^3 - 16362912 z^4 + 7937280 z^5 - 2238288 z^6 + 278460 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (672980 - 7571025 z - 21508416 z^2 + 21968296 z^3 - 16362912 z^4 + 7937280 z^5 - 2238288 z^6 + 278460 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (672980 - 7571025 z - 21508416 z^2 + 21968296 z^3 - 16362912 z^4 + 7937280 z^5 - 2238288 z^6 + 278460 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (672980 - 7571025 z - 21508416 z^2 + 21968296 z^3 - 16362912 z^4 + 7937280 z^5 - 2238288 z^6 + 278460 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (672980 - 7571025 z - 21508416 z^2 + 21968296 z^3 - 16362912 z^4 + 7937280 z^5 - 2238288 z^6 + 278460 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (672980 - 7907515 z + 35021904 z^2 - 23807816 z^3 + 24133384 z^4 - 17614176 z^5 + 8340384 z^6 - 2293980 z^7 + 278460 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (422463195 Pi Sqrt[1 + Sqrt[1 - z]] z^2)








Standard Form





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MathML Form







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<times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <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 /> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 278460 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2238288 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 7937280 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 16362912 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn 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Date Added to functions.wolfram.com (modification date)





2007-05-02