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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=-9/4, b>=a > For fixed z and a=-9/4, b=9/2





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









  


  








Input Form





Hypergeometric2F1[-(9/4), 9/2, 5, z] == (256 Sqrt[2] (2 (-1152 - 1344 z - 2580 z^2 - 8775 z^3 + 153725 z^4 - 238469 z^5 + 100947 z^6) EllipticE[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-1152 - 1344 z - 2580 z^2 - 8775 z^3 + 153725 z^4 - 238469 z^5 + 100947 z^6) EllipticE[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (1152 + 1920 z + 3720 z^2 + 11025 z^3 - 52250 z^4 + 33649 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (-1152 - 1344 z - 2580 z^2 - 8775 z^3 + 153725 z^4 - 238469 z^5 + 100947 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (-1152 - 1344 z - 2580 z^2 - 8775 z^3 + 153725 z^4 - 238469 z^5 + 100947 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (-1152 - 1344 z - 2580 z^2 - 8775 z^3 + 153725 z^4 - 238469 z^5 + 100947 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (12182625 Pi Sqrt[1 + Sqrt[1 - z]] z^4)








Standard Form





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MathML Form







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<sep /> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <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> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 100947 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 238469 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 153725 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8775 </cn> 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Rule Form





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





2007-05-02