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Mathematica Notation

Traditional Notation

Zeta Functions and Polylogarithms > Zeta[s,a] > Representations through equivalent functions > With related functions > With related functions > For zeta(s,a)




Input Form

ZetaClassical[s, a] == Zeta[s] - HarmonicNumber[a - 1, s]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["ZetaClassical", "[", RowBox[List["s", ",", "a"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Zeta", "[", "s", "]"]], "-", RowBox[List["HarmonicNumber", "[", RowBox[List[RowBox[List["a", "-", "1"]], ",", "s"]], "]"]]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mover> <mi> &#950; </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <mi> s </mi> <mo> , </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[OverscriptBox[&quot;\[Zeta]&quot;, &quot;^&quot;], &quot;(&quot;, RowBox[List[TagBox[&quot;s&quot;, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;a&quot;, Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[List[$CellContext`a, $CellContext`b], Zeta[$CellContext`a, $CellContext`b]]]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, TagBox[&quot;s&quot;, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[$CellContext`e, Zeta[$CellContext`e]]]] </annotation> </semantics> <mo> - </mo> <msubsup> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> </msubsup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Zeta </ci> <ci> s </ci> <ci> a </ci> </apply> <apply> <plus /> <apply> <ci> Zeta </ci> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> HarmonicNumber </ci> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> <ci> s </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ZetaClassical", "[", RowBox[List["s_", ",", "a_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Zeta", "[", "s", "]"]], "-", RowBox[List["HarmonicNumber", "[", RowBox[List[RowBox[List["a", "-", "1"]], ",", "s"]], "]"]]]]]]]]

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