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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=-11/2, b>=a > For fixed z and a=-11/2, b=19/4





http://functions.wolfram.com/07.23.03.a83k.01









  


  








Input Form





Hypergeometric2F1[-(11/2), 19/4, 2, z] == (-2 (14784 - 1904992 z + 17925120 z^2 - 59774720 z^3 + 91135980 z^4 - 65179530 z^5 + 17784975 z^6) EllipticE[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (14784 - 1904992 z + 17925120 z^2 - 59774720 z^3 + 91135980 z^4 - 65179530 z^5 + 17784975 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (14784 - 456160 z - 949280 z^2 + 18599360 z^3 - 50374740 z^4 + 50951550 z^5 - 17784975 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (14784 - 1904992 z + 17925120 z^2 - 59774720 z^3 + 91135980 z^4 - 65179530 z^5 + 17784975 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (14784 - 1904992 z + 17925120 z^2 - 59774720 z^3 + 91135980 z^4 - 65179530 z^5 + 17784975 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (14784 - 1904992 z + 17925120 z^2 - 59774720 z^3 + 91135980 z^4 - 65179530 z^5 + 17784975 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (360360 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z)








Standard Form





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MathML Form







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17784975 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 65179530 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 91135980 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 59774720 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 17925120 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1904992 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 14784 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> 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Rule Form





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





2007-05-02