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http://functions.wolfram.com/02.08.08.0002.01
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Glaisher == 2^(1/9) E^(EulerGamma/12) Pi^(1/12)
Product[(2 k + 1)^(1/(2 k + 1)^2), {k, 1, Infinity}]^(2/(3 Pi^2))
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Cell[BoxData[RowBox[List["Glaisher", "\[Equal]", RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "9"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["EulerGamma", "/", "12"]]], " ", SuperscriptBox["\[Pi]", RowBox[List["1", "/", "12"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[Infinity]"], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", "k"]], "+", "1"]], ")"]], FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", "k"]], "+", "1"]], ")"]], "2"]]]]], ")"]], FractionBox["2", RowBox[List["3", " ", SuperscriptBox["\[Pi]", "2"]]]]]]]]]]]
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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> <mi> A </mi> <annotation encoding='Mathematica'> TagBox["A", Function[List[], Glaisher]] </annotation> </semantics> <mo> ⩵ </mo> <mrow> <mroot> <mn> 2 </mn> <mn> 9 </mn> </mroot> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <semantics> <mi> ℽ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubledGamma]", Function[EulerGamma]] </annotation> </semantics> <mo> / </mo> <mn> 12 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> π </mi> <mn> 12 </mn> </mroot> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <munderover> <mo> ∏ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> ∞ </mi> </munderover> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mfrac> <mn> 1 </mn> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> </msup> </mrow> <mo> ) </mo> </mrow> <mfrac> <mn> 2 </mn> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <ci> Glaisher </ci> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 9 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <eulergamma /> <apply> <power /> <cn type='integer'> 12 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 12 </cn> </apply> <apply> <power /> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "Glaisher", "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "9"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["EulerGamma", "/", "12"]]], " ", SuperscriptBox["\[Pi]", RowBox[List["1", "/", "12"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[Infinity]"], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]], FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]], "2"]]]]], ")"]], FractionBox["2", RowBox[List["3", " ", SuperscriptBox["\[Pi]", "2"]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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