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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=-11/4, b>=a > For fixed z and a=-11/4, b=11/2





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









  


  








Input Form





Hypergeometric2F1[-(11/4), 11/2, 1, z] == (2 (1 - z)^(1/4) (161968 - 1812064 z + 5476380 z^2 - 6232200 z^3 + 2403375 z^4) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (161968 - 1812064 z + 5476380 z^2 - 6232200 z^3 + 2403375 z^4) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-1 + z) (51088 + 70720 z - 2028780 z^2 + 4309500 z^3 - 2403375 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (-161968 + 1812064 z - 5476380 z^2 + 6232200 z^3 - 2403375 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (-161968 + 1812064 z - 5476380 z^2 + 6232200 z^3 - 2403375 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (-161968 + 1812064 z - 5476380 z^2 + 6232200 z^3 - 2403375 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (27720 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] (-1 + z)^2)








Standard Form





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MathML Form







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/> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> z </ci> </apply> <apply> <power /> <apply> <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'> -2403375 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6232200 </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'> 5476380 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> 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Rule Form





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





2007-05-02