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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=-9/2, b>=a > For fixed z and a=-9/2, b=13/4





http://functions.wolfram.com/07.23.03.aa43.01









  


  










Input Form





Hypergeometric2F1[-(9/2), 13/4, 2, z] == (2 (1 - z)^(1/4) (-1120 + 107952 z - 615672 z^2 + 1215544 z^3 - 1009470 z^4 + 302841 z^5) EllipticE[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-1120 + 107952 z - 615672 z^2 + 1215544 z^3 - 1009470 z^4 + 302841 z^5) EllipticE[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (1120 - 107952 z + 615672 z^2 - 1215544 z^3 + 1009470 z^4 - 302841 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (1120 - 107952 z + 615672 z^2 - 1215544 z^3 + 1009470 z^4 - 302841 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (1120 - 107952 z + 615672 z^2 - 1215544 z^3 + 1009470 z^4 - 302841 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1120 - 53072 z + 257208 z^2 - 459952 z^3 + 355718 z^4 - 100947 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (13860 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z)










Standard Form





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MathML Form







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<times /> <cn type='integer'> 1215544 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 615672 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 107952 </cn> <ci> z </ci> </apply> <cn type='integer'> -1120 </cn> </apply> <apply> <ci> EllipticE </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> z </ci> </apply> <apply> 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Rule Form





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





2007-05-02