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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=-29/5, b>=a > For fixed z and a=-29/5, b=4





http://functions.wolfram.com/07.23.03.ao1y.01









  


  








Input Form





Hypergeometric2F1[-(29/5), 4, -(14/5), -z] == (1/15625) (2204 (291125/2204 - (48875 z)/266 + (206125 z^2)/399 - (80750 z^3)/21 - (191165 z^4)/6 - 36465 z^5 - 125/(1 + z) - 102 z^(19/5) (116 + 377 z + 286 z^2) Log[1 + z^(1/5)] - 102 (-1)^(4/5) z^(19/5) (116 + 377 z + 286 z^2) Log[1 - (-1)^(1/5) z^(1/5)] + 11832 (-1)^(3/5) z^(19/5) Log[1 + (-1)^(2/5) z^(1/5)] + 38454 (-1)^(3/5) z^(24/5) Log[1 + (-1)^(2/5) z^(1/5)] + 29172 (-1)^(3/5) z^(29/5) Log[1 + (-1)^(2/5) z^(1/5)] - 11832 (-1)^(2/5) z^(19/5) Log[1 - (-1)^(3/5) z^(1/5)] - 38454 (-1)^(2/5) z^(24/5) Log[1 - (-1)^(3/5) z^(1/5)] - 29172 (-1)^(2/5) z^(29/5) Log[1 - (-1)^(3/5) z^(1/5)] + 11832 (-1)^(1/5) z^(19/5) Log[1 + (-1)^(4/5) z^(1/5)] + 38454 (-1)^(1/5) z^(24/5) Log[1 + (-1)^(4/5) z^(1/5)] + 29172 (-1)^(1/5) z^(29/5) Log[1 + (-1)^(4/5) z^(1/5)]))








Standard Form





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MathML Form







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</mi> </mrow> <mn> 266 </mn> </mfrac> <mo> - </mo> <mfrac> <mn> 125 </mn> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> + </mo> <mfrac> <mn> 291125 </mn> <mn> 2204 </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'> 29 <sep /> 5 </cn> </apply> <cn type='integer'> 4 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 14 <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'> 2204 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 29172 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus 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type='integer'> 29172 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <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'> 29 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 36465 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 38454 </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'> 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'> 24 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 38454 </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> <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'> 24 <sep /> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 38454 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> 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</ci> <cn type='rational'> 19 <sep /> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 11832 </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'> 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'> 19 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 11832 </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> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 5 </cn> </apply> 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Rule Form





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





2007-05-02