Riemann zeta function: Specific values (formula 10.01.03.0037)

Zeta

$Mathematica Notation$

Zeta Functions and Polylogarithms

Zeta[s]

Specific values

Values at fixed points

http://functions.wolfram.com/10.01.03.0037.01

Input Form

Zeta[22] == (155366 Pi^22)/13447856940643125

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Zeta", "[", "22", "]"]], "\[Equal]", FractionBox[RowBox[List["155366", " ", SuperscriptBox["\[Pi]", "22"]]], "13447856940643125"]]]]]

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> 22 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["22", Rule[Editable, True]], ")"]], InterpretTemplate[Function[$CellContext`e, Zeta[$CellContext`e]]]] </annotation> </semantics> <mo> ⩵ </mo> <mfrac> <mrow> <mn> 155366 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 22 </mn> </msup> </mrow> <mn> 13447856940643125 </mn> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Zeta </ci> <cn type='integer'> 22 </cn> </apply> <apply> <times /> <cn type='integer'> 155366 </cn> <apply> <power /> <pi /> <cn type='integer'> 22 </cn> </apply> <apply> <power /> <cn type='integer'> 13447856940643125 </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", "[", "22", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["155366", " ", SuperscriptBox["\[Pi]", "22"]]], "13447856940643125"]]]]]

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

2001-10-29

Zeta[s,a]