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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=-7/4





http://functions.wolfram.com/07.23.03.9279.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(7/4), -(3/2), z] == (1/(2340 Pi^(3/2))) ((4 Sqrt[z] (585 - 3705 z - 31521 z^2 + 20937 z^3 - 8120 z^4 + 1344 z^5) EllipticE[(1/2) (1 - Sqrt[z])] + 4 Sqrt[z] (-585 + 3705 z + 31521 z^2 - 20937 z^3 + 8120 z^4 - 1344 z^5) EllipticE[(1/2) (1 + Sqrt[z])] + (2340 - 1170 Sqrt[z] - 16575 z + 7410 z^(3/2) + 61425 z^2 + 63042 z^(5/2) - 9429 z^3 - 41874 z^(7/2) + 3871 z^4 + 16240 z^(9/2) - 672 z^5 - 2688 z^(11/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (2340 + 1170 Sqrt[z] - 16575 z - 7410 z^(3/2) + 61425 z^2 - 63042 z^(5/2) - 9429 z^3 + 41874 z^(7/2) + 3871 z^4 - 16240 z^(9/2) - 672 z^5 + 2688 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> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 61425 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 7410 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 16575 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 1170 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 2340 </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