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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=-3/8, b>=a > For fixed z and a=-3/8, b=2





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









  


  








Input Form





Hypergeometric2F1[-(3/8), 2, 13/8, -z] == -((1/(512 z^(5/8))) (5 (-1)^(1/8) (88 (-1)^(7/8) z^(5/8) - 3 (-1)^(1/4) (3 + 11 z) Log[1 - (-1)^(1/8) z^(1/8)] + 3 (-1)^(1/4) (3 + 11 z) Log[1 + (-1)^(1/8) z^(1/8)] + 9 Log[1 - (-1)^(3/8) z^(1/8)] + 33 z Log[1 - (-1)^(3/8) z^(1/8)] - 9 Log[1 + (-1)^(3/8) z^(1/8)] - 33 z Log[1 + (-1)^(3/8) z^(1/8)] + 9 (-1)^(3/4) Log[1 - (-1)^(5/8) z^(1/8)] + 33 (-1)^(3/4) z Log[1 - (-1)^(5/8) z^(1/8)] - 9 (-1)^(3/4) Log[1 + (-1)^(5/8) z^(1/8)] - 33 (-1)^(3/4) z Log[1 + (-1)^(5/8) z^(1/8)] - 9 I Log[1 - (-1)^(7/8) z^(1/8)] - 33 I z Log[1 - (-1)^(7/8) z^(1/8)] + 9 I Log[1 + (-1)^(7/8) z^(1/8)] + 33 I z Log[1 + (-1)^(7/8) z^(1/8)])))








Standard Form





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MathML Form







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</mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> &#8290; </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 88 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </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'> 3 <sep /> 8 </cn> </apply> <cn type='integer'> 2 </cn> </list> <list> <cn type='rational'> 13 <sep /> 8 </cn> </list> <apply> 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<ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 9 </cn> <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 /> 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 /> <cn type='integer'> 33 </cn> <ci> z </ci> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <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 /> <cn type='integer'> 9 </cn> <apply> 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type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 8 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 33 </cn> <imaginaryi /> <ci> z </ci> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <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> <times /> <cn type='integer'> 9 </cn> <imaginaryi /> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <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> <times /> <cn type='integer'> 88 </cn> <apply> <power /> <cn 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Rule Form





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





2007-05-02