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variants of this functions
PolyLog






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > PolyLog[nu,p,z] > Identities > Functional identities





http://functions.wolfram.com/10.09.17.0002.01









  


  










Input Form





PolyLog[n, p, z] == (-1)^n Sum[(-1)^k Sum[(Log[-z]^j Binomial[n + k - j - 1, k - j] PolyLog[n + k - j, p - k, 1/z])/j!, {j, 0, k}], {k, 0, p - 1}] + (-1)^p (Sum[(Log[-z]^j c[n - j, p])/j!, {j, 0, n - 1}] + Log[-z]^(n + p)/(n + p)!) /; c[n, p] == (1 - (-1)^n) (-1)^p PolyLog[n, p, -1] - (-1)^n Sum[Binomial[n + j - 1, j] (-1)^(p - j) PolyLog[n + j, p - j, -1], {j, 1, p - 1}] && Element[n, Integers] && n > 0 && Element[p, Integers] && p > 0 && !IntervalMemberQ[Interval[{0, 1}], z]










Standard Form





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MathML Form







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</mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow> <mi> p </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mrow> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mrow> <mi> j </mi> <mo> + </mo> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mi> j </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[RowBox[List[&quot;j&quot;, &quot;+&quot;, &quot;n&quot;, &quot;-&quot;, &quot;1&quot;]], Identity, Rule[Editable, True]]], List[TagBox[&quot;j&quot;, Identity, Rule[Editable, True]]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] </annotation> </semantics> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> p </mi> <mo> - </mo> <mi> j </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mstyle scriptlevel='0'> <msubsup> <semantics> <mi> S </mi> <annotation encoding='Mathematica'> TagBox[&quot;S&quot;, StirlingS1] </annotation> </semantics> <mrow> <mi> n </mi> <mo> + </mo> <mi> j </mi> </mrow> <mrow> <mi> p </mi> <mo> - </mo> <mi> j </mi> </mrow> </msubsup> </mstyle> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> &#8743; 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</mo> <mrow> <mi> z </mi> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29





© 1998- Wolfram Research, Inc.