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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/07.23.03.9275.01









  


  








Input Form





Hypergeometric2F1[-(23/4), -(7/4), -(7/2), z] == (1/(400 Pi^(3/2))) ((8 Sqrt[z] (50 - 125 z + 60 z^2 + 35 z^3 - 212 z^4 + 96 z^5) EllipticE[(1/2) (1 - Sqrt[z])] - 8 Sqrt[z] (50 - 125 z + 60 z^2 + 35 z^3 - 212 z^4 + 96 z^5) EllipticE[(1/2) (1 + Sqrt[z])] + (400 - 200 Sqrt[z] - 1300 z + 500 z^(3/2) + 1185 z^2 - 240 z^(5/2) + 10 z^3 - 140 z^(7/2) + 185 z^4 + 848 z^(9/2) - 96 z^5 - 384 z^(11/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (400 + 200 Sqrt[z] - 1300 z - 500 z^(3/2) + 1185 z^2 + 240 z^(5/2) + 10 z^3 + 140 z^(7/2) + 185 z^4 - 848 z^(9/2) - 96 z^5 + 384 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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<cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 500 </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'> 1300 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 200 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 400 </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