Riemann zeta function: Specific values (formula 10.01.03.0040)

Zeta

$Mathematica Notation$

Zeta Functions and Polylogarithms

Zeta[s]

Specific values

Values at fixed points

http://functions.wolfram.com/10.01.03.0040.01

Input Form

Zeta[28] == (6785560294 Pi^28)/564653660170076273671875

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Zeta", "[", "28", "]"]], "\[Equal]", FractionBox[RowBox[List["6785560294", " ", SuperscriptBox["\[Pi]", "28"]]], "564653660170076273671875"]]]]]

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> 28 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", "28", ")"]], InterpretTemplate[Function[$CellContext`e, Zeta[$CellContext`e]]]] </annotation> </semantics> <mo> ⩵ </mo> <mfrac> <mrow> <mn> 6785560294 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 28 </mn> </msup> </mrow> <mn> 564653660170076273671875 </mn> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 28 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", "28", ")"]], InterpretTemplate[Function[$CellContext`e, Zeta[$CellContext`e]]]] </annotation> </semantics> <mo> ⩵ </mo> <mfrac> <mrow> <mn> 6785560294 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 28 </mn> </msup> </mrow> <mn> 564653660170076273671875 </mn> </mfrac> </mrow> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Zeta", "[", "28", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["6785560294", " ", SuperscriptBox["\[Pi]", "28"]]], "564653660170076273671875"]]]]]

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

2001-10-29

Zeta[s,a]