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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=21/4, b>=a > For fixed z and a=21/4, b=21/4





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









  


  










Input Form





Hypergeometric2F1[21/4, 21/4, 7/2, z] == (1/(2197845 Pi^(3/2) z^(5/2))) (8 ((2 (1764 - 21021 z + 221823 z^2 + 646601 z^3 + 133873 z^4) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^7 - (2 (1764 - 21021 z + 221823 z^2 + 646601 z^3 + 133873 z^4) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^7 - (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^6)) ((1764 - 882 Sqrt[z] - 20139 z + 9702 z^(3/2) + 212121 z^2 + 172682 z^(5/2) + 473919 z^3 + 64258 z^(7/2) + 69615 z^4) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^7)) ((1764 + 882 Sqrt[z] - 20139 z - 9702 z^(3/2) + 212121 z^2 - 172682 z^(5/2) + 473919 z^3 - 64258 z^(7/2) + 69615 z^4) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)










Standard Form





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MathML Form







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<sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 212121 </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'> 9702 </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'> 20139 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 882 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 1764 </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> </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