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http://functions.wolfram.com/10.01.03.0030.01
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Zeta[15] == (13687 Pi^15)/390769879500 -
2 Sum[1/(k^15 (E^(2 Pi k) - 1)), {k, 1, Infinity}]
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Cell[BoxData[RowBox[List[RowBox[List["Zeta", "[", "15", "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["13687", SuperscriptBox["\[Pi]", "15"]]], "390769879500"], "-", RowBox[List["2", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox["1", RowBox[List[SuperscriptBox["k", "15"], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", "\[Pi]", " ", "k"]]], "-", "1"]], ")"]]]]]]]]]]]]]]]
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<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> 15 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["15", Rule[Editable, True]], ")"]], InterpretTemplate[Function[$CellContext`e, Zeta[$CellContext`e]]]] </annotation> </semantics> <mo> ⩵ </mo> <mrow> <mfrac> <mrow> <mn> 13687 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 15 </mn> </msup> </mrow> <mn> 390769879500 </mn> </mfrac> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> ∞ </mi> </munderover> <mfrac> <mn> 1 </mn> <mrow> <msup> <mi> k </mi> <mn> 15 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Zeta </ci> <cn type='integer'> 15 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 13687 </cn> <apply> <power /> <pi /> <cn type='integer'> 15 </cn> </apply> <apply> <power /> <cn type='integer'> 390769879500 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <ci> k </ci> <cn type='integer'> 15 </cn> </apply> <apply> <plus /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> <ci> k </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Zeta", "[", "15", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["13687", " ", SuperscriptBox["\[Pi]", "15"]]], "390769879500"], "-", RowBox[List["2", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox["1", RowBox[List[SuperscriptBox["k", "15"], " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[Pi]", " ", "k"]]], "-", "1"]], ")"]]]]]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
