Riemann zeta function: Specific values (formula 10.01.03.0019)

Zeta

$Mathematica Notation$

Zeta Functions and Polylogarithms

Zeta[s]

Specific values

Values at fixed points

http://functions.wolfram.com/10.01.03.0019.01

Input Form

Zeta[4] == Pi^4/90

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Zeta", "[", "4", "]"]], "\[Equal]", FractionBox[SuperscriptBox["\[Pi]", "4"], "90"]]]]]

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> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 4 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["4", Rule[Editable, True]], ")"]], InterpretTemplate[Function[$CellContext`e, Zeta[$CellContext`e]]]] </annotation> </semantics> <mo> ⩵ </mo> <mfrac> <msup> <mi> π </mi> <mn> 4 </mn> </msup> <mn> 90 </mn> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Zeta </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <cn type='integer'> 90 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Zeta", "[", "4", "]"]], "]"]], "\[RuleDelayed]", FractionBox[SuperscriptBox["\[Pi]", "4"], "90"]]]]]

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

2001-10-29

Zeta[s,a]