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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=-3/4





http://functions.wolfram.com/07.23.03.9371.01









  


  








Input Form





Hypergeometric2F1[-(23/4), -(3/4), -(1/2), z] == (1/(6630 Pi^(3/2))) ((2 Sqrt[z] (3315 + 98835 z - 121119 z^2 + 90169 z^3 - 36384 z^4 + 6144 z^5) EllipticE[(1/2) (1 - Sqrt[z])] - 2 Sqrt[z] (3315 + 98835 z - 121119 z^2 + 90169 z^3 - 36384 z^4 + 6144 z^5) EllipticE[(1/2) (1 + Sqrt[z])] - (-6630 + 3315 Sqrt[z] + 59670 z + 98835 z^(3/2) - 25170 z^2 - 121119 z^(5/2) + 20218 z^3 + 90169 z^(7/2) - 8664 z^4 - 36384 z^(9/2) + 1536 z^5 + 6144 z^(11/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (6630 + 3315 Sqrt[z] - 59670 z + 98835 z^(3/2) + 25170 z^2 - 121119 z^(5/2) - 20218 z^3 + 90169 z^(7/2) + 8664 z^4 - 36384 z^(9/2) - 1536 z^5 + 6144 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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type='rational'> 5 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 25170 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 98835 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 59670 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 3315 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -6630 </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> <apply> <times /> <apply> <plus /> <apply> <times /> <cn 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/> <cn type='integer'> 121119 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 25170 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 98835 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 59670 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 3315 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 6630 </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