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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 8 and fixed z and a<0 > For fixed z and a=-21/8, b>=a > For fixed z and a=-21/8, b=5





http://functions.wolfram.com/07.23.03.bm2m.01









  


  










Input Form





Hypergeometric2F1[-(21/8), 5, -(5/8), -z] == (1/2097152) (91 ((64 (5843 + 10710 z + 4995 z^2))/(1 + z)^3 - 1013985 (-(8/13) + (8 z)/5 + (-1)^(1/8) z^(13/8) (I Log[1 - (-1)^(1/8) z^(1/8)] - I Log[1 + (-1)^(1/8) z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(3/8) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(3/8) z^(1/8)] - Log[1 - (-1)^(5/8) z^(1/8)] + Log[1 + (-1)^(5/8) z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(7/8) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(7/8) z^(1/8)])) + 2559105 (-(8/21) + (8 z)/13 - (8 z^2)/5 + (-1)^(1/8) z^(21/8) ((-I) Log[1 - (-1)^(1/8) z^(1/8)] + I Log[1 + (-1)^(1/8) z^(1/8)] + (-1)^(3/4) Log[1 - (-1)^(3/8) z^(1/8)] - (-1)^(3/4) Log[1 + (-1)^(3/8) z^(1/8)] + Log[1 - (-1)^(5/8) z^(1/8)] - Log[1 + (-1)^(5/8) z^(1/8)] - (-1)^(1/4) Log[1 - (-1)^(7/8) z^(1/8)] + (-1)^(1/4) Log[1 + (-1)^(7/8) z^(1/8)]))))










Standard Form





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MathML Form







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</mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 21 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mfrac> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mn> 5 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mn> 13 </mn> </mfrac> <mo> - </mo> <mfrac> <mn> 8 </mn> <mn> 21 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </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'> 21 <sep /> 8 </cn> </apply> <cn type='integer'> 5 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 5 <sep /> 8 </cn> </apply> </list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2097152 </cn> <apply> <times /> <cn type='integer'> 91 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 64 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 4995 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 10710 </cn> <ci> z </ci> </apply> <cn type='integer'> 5843 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1013985 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <plus /> <apply> <times /> <imaginaryi /> <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'> 1 <sep /> 8 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 4 </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 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<power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 8 <sep /> 13 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2559105 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </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'> 1 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Rule Form





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





2007-05-02