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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=3





http://functions.wolfram.com/07.23.03.ap76.01









  


  








Input Form





Hypergeometric2F1[-(26/5), 3, -(6/5), -z] == (1/15625) (15625 - 203125 z + 8531250 z^2 + 53511640 z^3 + 89369280 z^4 + 44684640 z^5 - 48048 z^(11/5) (56 + 273 z + 403 z^2 + 186 z^3) Log[1 + z^(1/5)] + 48048 (-1)^(1/5) z^(11/5) (56 + 273 z + 403 z^2 + 186 z^3) Log[1 - (-1)^(1/5) z^(1/5)] - 2690688 (-1)^(2/5) z^(11/5) Log[1 + (-1)^(2/5) z^(1/5)] - 13117104 (-1)^(2/5) z^(16/5) Log[1 + (-1)^(2/5) z^(1/5)] - 19363344 (-1)^(2/5) z^(21/5) Log[1 + (-1)^(2/5) z^(1/5)] - 8936928 (-1)^(2/5) z^(26/5) Log[1 + (-1)^(2/5) z^(1/5)] + 2690688 (-1)^(3/5) z^(11/5) Log[1 - (-1)^(3/5) z^(1/5)] + 13117104 (-1)^(3/5) z^(16/5) Log[1 - (-1)^(3/5) z^(1/5)] + 19363344 (-1)^(3/5) z^(21/5) Log[1 - (-1)^(3/5) z^(1/5)] + 8936928 (-1)^(3/5) z^(26/5) Log[1 - (-1)^(3/5) z^(1/5)] - 2690688 (-1)^(4/5) z^(11/5) Log[1 + (-1)^(4/5) z^(1/5)] - 13117104 (-1)^(4/5) z^(16/5) Log[1 + (-1)^(4/5) z^(1/5)] - 19363344 (-1)^(4/5) z^(21/5) Log[1 + (-1)^(4/5) z^(1/5)] - 8936928 (-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> </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> <mrow> <mn> 8531250 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 203125 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 15625 </mn> </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'> 3 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 6 <sep /> 5 </cn> </apply> </list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 15625 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -8936928 </cn> <apply> <power /> <cn type='integer'> -1 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Rule Form





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





2007-05-02