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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.amok.01









  


  








Input Form





Hypergeometric2F1[15/4, 15/4, 7/2, z] == (1/(17787 Pi^(3/2) z^(5/2))) (10 ((4 Sqrt[z] (-3 + 14 z + 181 z^2) EllipticE[(1/2) (1 - Sqrt[z])])/ (-1 + z)^4 + (4 Sqrt[z] (-3 + 14 z + 181 z^2) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^4 - ((12 - 18 Sqrt[z] - 47 z + 75 z^(3/2) + 131 z^2 + 231 z^(5/2)) EllipticK[(1/2) (1 - Sqrt[z])])/((-1 + Sqrt[z])^4 (1 + Sqrt[z])^3) + ((-12 - 18 Sqrt[z] + 47 z + 75 z^(3/2) - 131 z^2 + 231 z^(5/2)) EllipticK[(1/2) (1 + Sqrt[z])])/((-1 + Sqrt[z])^3 (1 + Sqrt[z])^4)) Gamma[1/4]^2)








Standard Form





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MathML Form







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</apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 181 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 14 </cn> <ci> z </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <ci> EllipticE </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> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 231 </cn> <apply> <power 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02