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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=13/4, b>=a > For fixed z and a=13/4, b=17/4





http://functions.wolfram.com/07.23.03.amc2.01









  


  








Input Form





Hypergeometric2F1[13/4, 17/4, 1/2, z] == (1/(585 Pi^(3/2))) (((2 Sqrt[z] (8601 + 38325 z + 18379 z^2 + 231 z^3) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^7 - (2 Sqrt[z] (8601 + 38325 z + 18379 z^2 + 231 z^3) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^7 - (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^6)) ((585 + 8016 Sqrt[z] + 8277 z + 30048 z^(3/2) + 7291 z^2 + 11088 z^(5/2) + 231 z^3) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^7)) ((585 - 8016 Sqrt[z] + 8277 z - 30048 z^(3/2) + 7291 z^2 - 11088 z^(5/2) + 231 z^3) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)








Standard Form





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MathML Form







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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> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 7 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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