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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=1/4





http://functions.wolfram.com/07.23.03.9459.01









  


  








Input Form





Hypergeometric2F1[-(23/4), 1/4, -(5/2), z] == (1/(1800 Pi^(3/2))) ((2 Sqrt[z] (900 + 855 z + 1425 z^2 - 62988 z^3 + 98304 z^4 - 40960 z^5) EllipticE[(1/2) (1 - Sqrt[z])] + 2 Sqrt[z] (-900 - 855 z - 1425 z^2 + 62988 z^3 - 98304 z^4 + 40960 z^5) EllipticE[(1/2) (1 + Sqrt[z])] + (1800 - 900 Sqrt[z] + 360 z - 855 z^(3/2) + 1365 z^2 - 1425 z^(5/2) + 10395 z^3 + 62988 z^(7/2) - 21696 z^4 - 98304 z^(9/2) + 10240 z^5 + 40960 z^(11/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (1800 + 900 Sqrt[z] + 360 z + 855 z^(3/2) + 1365 z^2 + 1425 z^(5/2) + 10395 z^3 - 62988 z^(7/2) - 21696 z^4 + 98304 z^(9/2) + 10240 z^5 - 40960 z^(11/2)) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)








Standard Form





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MathML Form







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</apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 855 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 360 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 900 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 1800 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -40960 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> 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</apply> </apply> <apply> <times /> <cn type='integer'> 855 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 360 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 900 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 1800 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02