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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=5/4, b>=a > For fixed z and a=5/4, b=9/4





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









  


  










Input Form





Hypergeometric2F1[5/4, 9/4, -(11/2), z] == (1/(73920 Pi^(3/2))) (((1/(-1 + z)^9) (2 Sqrt[z] (-36960 + 337680 z - 1392678 z^2 + 3449571 z^3 - 5840304 z^4 + 7720746 z^5 + 53573678 z^6 + 908523 z^7) EllipticE[(1/2) (1 - Sqrt[z])]) - (1/(-1 + z)^9) (2 Sqrt[z] (-36960 + 337680 z - 1392678 z^2 + 3449571 z^3 - 5840304 z^4 + 7720746 z^5 + 53573678 z^6 + 908523 z^7) EllipticE[(1/2) (1 + Sqrt[z])]) - (1/((-1 + Sqrt[z])^9 (1 + Sqrt[z])^8)) ((73920 - 110880 Sqrt[z] - 619920 z + 957600 z^(3/2) + 2325960 z^2 - 3718638 z^(5/2) - 5197701 z^3 + 8647272 z^(7/2) + 7929684 z^4 - 13769988 z^(9/2) - 9790206 z^5 + 17510952 z^(11/2) + 19049804 z^6 + 34523874 z^(13/2) + 908523 z^7) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^8 (1 + Sqrt[z])^9)) ((73920 + 110880 Sqrt[z] - 619920 z - 957600 z^(3/2) + 2325960 z^2 + 3718638 z^(5/2) - 5197701 z^3 - 8647272 z^(7/2) + 7929684 z^4 + 13769988 z^(9/2) - 9790206 z^5 - 17510952 z^(11/2) + 19049804 z^6 - 34523874 z^(13/2) + 908523 z^7) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)










Standard Form





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MathML Form







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</cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 337680 </cn> <ci> z </ci> </apply> <cn type='integer'> -36960 </cn> </apply> <apply> <ci> EllipticE </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 9 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 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Rule Form





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





2007-05-02