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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=15/4, b>=a > For fixed z and a=15/4, b=15/4





http://functions.wolfram.com/07.23.03.amo8.01









  


  








Input Form





Hypergeometric2F1[15/4, 15/4, 1/2, z] == (1/(71148 Pi^(3/2))) ((-((2 (17787 + 349455 z + 527729 z^2 + 88069 z^3) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^7) - (2 (17787 + 349455 z + 527729 z^2 + 88069 z^3) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^7 + (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^6)) ((17787 + 48144 Sqrt[z] + 301311 z + 154592 z^(3/2) + 373137 z^2 + 43024 z^(5/2) + 45045 z^3) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^7)) ((-17787 + 48144 Sqrt[z] - 301311 z + 154592 z^(3/2) - 373137 z^2 + 43024 z^(5/2) - 45045 z^3) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)








Standard Form





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MathML Form







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z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 154592 </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'> 301311 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 48144 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -17787 </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> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <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