Riemann-Siegel function Z: Specific values (formula 10.04.03.0006)

RiemannSiegelZ

$Mathematica Notation$

Zeta Functions and Polylogarithms

RiemannSiegelZ[z]

Specific values

Values at fixed points

http://functions.wolfram.com/10.04.03.0006.01

Input Form

RiemannSiegelZ[0] == Zeta[1/2]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["RiemannSiegelZ", "[", "0", "]"]], "\[Equal]", RowBox[List["Zeta", "[", FractionBox["1", "2"], "]"]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mi> Z </mi> <annotation encoding='Mathematica'> TagBox["Z", RiemannSiegelZ] </annotation> </semantics> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox[FractionBox["1", "2"], Rule[Editable, True]], ")"]], InterpretTemplate[Function[$CellContext`e, Zeta[$CellContext`e]]]] </annotation> </semantics> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> RiemannSiegelZ </ci> <cn type='integer'> 0 </cn> </apply> <apply> <ci> Zeta </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["RiemannSiegelZ", "[", "0", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Zeta", "[", FractionBox["1", "2"], "]"]]]]]]

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

2001-10-29