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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=-27/5, b>=a > For fixed z and a=-27/5, b=4





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









  


  










Input Form





Hypergeometric2F1[-(27/5), 4, -(12/5), -z] == (1/15625) (1683 (226000/1683 - (39000 z)/187 + (93000 z^2)/119 - (79000 z^3)/7 - 62160 z^4 - 62160 z^5 - 125/(1 + z) - 96 z^(17/5) (99 + 333 z + 259 z^2) Log[1 + z^(1/5)] - 96 (-1)^(2/5) z^(17/5) (99 + 333 z + 259 z^2) Log[1 - (-1)^(1/5) z^(1/5)] - 9504 (-1)^(4/5) z^(17/5) Log[1 + (-1)^(2/5) z^(1/5)] - 31968 (-1)^(4/5) z^(22/5) Log[1 + (-1)^(2/5) z^(1/5)] - 24864 (-1)^(4/5) z^(27/5) Log[1 + (-1)^(2/5) z^(1/5)] + 9504 (-1)^(1/5) z^(17/5) Log[1 - (-1)^(3/5) z^(1/5)] + 31968 (-1)^(1/5) z^(22/5) Log[1 - (-1)^(3/5) z^(1/5)] + 24864 (-1)^(1/5) z^(27/5) Log[1 - (-1)^(3/5) z^(1/5)] + 9504 (-1)^(3/5) z^(17/5) Log[1 + (-1)^(4/5) z^(1/5)] + 31968 (-1)^(3/5) z^(22/5) Log[1 + (-1)^(4/5) z^(1/5)] + 24864 (-1)^(3/5) z^(27/5) Log[1 + (-1)^(4/5) z^(1/5)]))










Standard Form





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MathML Form







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<mn> 187 </mn> </mfrac> <mo> - </mo> <mfrac> <mn> 125 </mn> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> + </mo> <mfrac> <mn> 226000 </mn> <mn> 1683 </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'> 27 <sep /> 5 </cn> </apply> <cn type='integer'> 4 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 12 <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> <times /> <cn type='integer'> 1683 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -24864 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 4 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <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'> 27 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 24864 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 27 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 24864 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 4 <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'> 27 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 62160 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 31968 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 4 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 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4 <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'> 22 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 62160 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 96 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 259 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 333 </cn> <ci> z </ci> </apply> <cn type='integer'> 99 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 17 <sep /> 5 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Rule Form





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





2007-05-02