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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 5 and fixed z > For fixed z and a=-26/5, b>=a > For fixed z and a=-26/5, b=5





http://functions.wolfram.com/07.23.03.apb9.01









  


  








Input Form





Hypergeometric2F1[-(26/5), 5, -(6/5), z] == (1/390625) (4004 (-(2111875/4004) - 625/(-1 + z) + (1375625 z)/924 + (5831875 z^2)/44 - (13058130 z^3)/11 + 2681810 z^4 - 1753980 z^5 - 124 z^(11/5) (-364 + 2457 z - 4797 z^2 + 2829 z^3) Log[1 - z^(1/5)] + 124 (-1)^(1/5) z^(11/5) (-364 + 2457 z - 4797 z^2 + 2829 z^3) Log[1 + (-1)^(1/5) z^(1/5)] + 45136 (-1)^(2/5) z^(11/5) Log[1 - (-1)^(2/5) z^(1/5)] - 304668 (-1)^(2/5) z^(16/5) Log[1 - (-1)^(2/5) z^(1/5)] + 594828 (-1)^(2/5) z^(21/5) Log[1 - (-1)^(2/5) z^(1/5)] - 350796 (-1)^(2/5) z^(26/5) Log[1 - (-1)^(2/5) z^(1/5)] - 45136 (-1)^(3/5) z^(11/5) Log[1 + (-1)^(3/5) z^(1/5)] + 304668 (-1)^(3/5) z^(16/5) Log[1 + (-1)^(3/5) z^(1/5)] - 594828 (-1)^(3/5) z^(21/5) Log[1 + (-1)^(3/5) z^(1/5)] + 350796 (-1)^(3/5) z^(26/5) Log[1 + (-1)^(3/5) z^(1/5)] + 45136 (-1)^(4/5) z^(11/5) Log[1 - (-1)^(4/5) z^(1/5)] - 304668 (-1)^(4/5) z^(16/5) Log[1 - (-1)^(4/5) z^(1/5)] + 594828 (-1)^(4/5) z^(21/5) Log[1 - (-1)^(4/5) z^(1/5)] - 350796 (-1)^(4/5) z^(26/5) Log[1 - (-1)^(4/5) z^(1/5)]))








Standard Form





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MathML Form







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<mn> 5 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 11 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 5831875 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mn> 44 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 1375625 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mn> 924 </mn> </mfrac> <mo> - </mo> <mfrac> <mn> 625 </mn> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> - </mo> <mfrac> <mn> 2111875 </mn> <mn> 4004 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 26 <sep /> 5 </cn> </apply> <cn type='integer'> 5 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 6 <sep /> 5 </cn> </apply> </list> 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</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'> 4797 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2457 </cn> <ci> z </ci> </apply> <cn type='integer'> -364 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 45136 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> 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Date Added to functions.wolfram.com (modification date)





2007-05-02