PolyLog[\[Nu], p, z] == Integrate[PolyLog[\[Nu] - 1, p, t]/t, {t, 0, z}]

Cell[BoxData[RowBox[List[RowBox[List["PolyLog", "[", RowBox[List["\[Nu]", ",", "p", ",", "z"]], "]"]], "\[Equal]", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "z"], RowBox[List[FractionBox[RowBox[List["PolyLog", "[", RowBox[List[RowBox[List["\[Nu]", "-", "1"]], ",", "p", ",", "t"]], "]"]], "t"], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <semantics> <mi> S </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mrow> <mi> &#957; </mi> <mo> , </mo> <mi> p </mi> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msubsup> <mo> &#8747; </mo> <mn> 0 </mn> <mi> z </mi> </msubsup> <mrow> <mfrac> <mn> 1 </mn> <mi> t </mi> </mfrac> <mo> &#8290; </mo> <mrow> <mstyle scriptlevel='0'> <msubsup> <semantics> <mi> S </mi> <annotation encoding='Mathematica'> TagBox[&quot;S&quot;, StirlingS1] </annotation> </semantics> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mi> p </mi> </msubsup> </mstyle> <mo> ( </mo> <mi> t </mi> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> t </mi> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> PolyLog </ci> <ci> &#957; </ci> <ci> p </ci> <ci> z </ci> </apply> <apply> <int /> <bvar> <ci> t </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> z </ci> </uplimit> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> t </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <apply> <ci> StirlingS1 </ci> <ci> S </ci> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> p </ci> </apply> <ci> t </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["PolyLog", "[", RowBox[List["\[Nu]_", ",", "p_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "z"], RowBox[List[FractionBox[RowBox[List["PolyLog", "[", RowBox[List[RowBox[List["\[Nu]", "-", "1"]], ",", "p", ",", "t"]], "]"]], "t"], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]

2001-10-29