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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=7/4, b>=a > For fixed z and a=7/4, b=7/4





http://functions.wolfram.com/07.23.03.akd9.01









  


  








Input Form





Hypergeometric2F1[7/4, 7/4, -(3/2), z] == (1/(144 Pi^(3/2))) ((-((2 (36 - 249 z + 1254 z^2 + 1007 z^3) EllipticE[(1/2) (1 - Sqrt[z])])/ (-1 + z)^5) - (2 (36 - 249 z + 1254 z^2 + 1007 z^3) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^5 + ((36 - 18 Sqrt[z] - 231 z + 108 z^(3/2) + 1146 z^2 + 422 z^(5/2) + 585 z^3) EllipticK[(1/2) (1 - Sqrt[z])])/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^4) + ((-36 - 18 Sqrt[z] + 231 z + 108 z^(3/2) - 1146 z^2 + 422 z^(5/2) - 585 z^3) EllipticK[(1/2) (1 + Sqrt[z])])/ ((-1 + Sqrt[z])^4 (1 + Sqrt[z])^5)) Gamma[1/4]^2)








Standard Form





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MathML Form







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-36 </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> <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'> 4 </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'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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