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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=-3/2, b>=a > For fixed z and a=-3/2, b=1/4





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









  


  








Input Form





Hypergeometric2F1[-(3/2), 1/4, 6, z] == (128 Sqrt[2] (-2 (1 - z)^(1/4) (-8192 + 60160 z - 195664 z^2 + 380816 z^3 - 561220 z^4 - 277970 z^5 + 21945 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (-8192 + 60160 z - 195664 z^2 + 380816 z^3 - 561220 z^4 - 277970 z^5 + 21945 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-8192 + 64256 z - 224976 z^2 + 473392 z^3 - 735860 z^4 + 1004190 z^5 + 7315 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (-8192 + 60160 z - 195664 z^2 + 380816 z^3 - 561220 z^4 - 277970 z^5 + 21945 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (-8192 + 60160 z - 195664 z^2 + 380816 z^3 - 561220 z^4 - 277970 z^5 + 21945 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (-8192 + 60160 z - 195664 z^2 + 380816 z^3 - 561220 z^4 - 277970 z^5 + 21945 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (65900835 Pi Sqrt[1 + Sqrt[1 - z]] z^5)








Standard Form





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MathML Form







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<apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 277970 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 561220 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 380816 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 195664 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 60160 </cn> <ci> z </ci> </apply> <cn type='integer'> -8192 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> 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Rule Form





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





2007-05-02