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http://functions.wolfram.com/10.01.26.0004.01
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Zeta[n] == (1/(1 - 2^(1 - n)))
MeijerG[{{1, 1 + Subscript[a, 1], \[Ellipsis], 1 + Subscript[a, n]}, {}},
{{1}, {Subscript[a, 1], \[Ellipsis], Subscript[a, n]}}, 1] /;
Subscript[a, 1] == Subscript[a, 2] == \[Ellipsis] == Subscript[a, n] == 0 &&
Element[n - 1, Integers] && n - 1 > 0
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Zeta", "[", "n", "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["1", "-", SuperscriptBox["2", RowBox[List["1", "-", "n"]]]]]], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", ",", RowBox[List["1", "+", SubscriptBox["a", "1"]]], ",", "\[Ellipsis]", ",", RowBox[List["1", "+", SubscriptBox["a", "n"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "n"]]], "}"]]]], "}"]], ",", "1"]], "]"]]]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["a", "1"], "\[Equal]", SubscriptBox["a", "2"], "\[Equal]", "\[Ellipsis]", "\[Equal]", SubscriptBox["a", "n"], "\[Equal]", "0"]], "\[And]", RowBox[List[RowBox[List["n", "-", "1"]], "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List["n", "-", "1"]], ">", "0"]]]]]]]]
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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> <mrow> <mrow> <mi> ζ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mn> 2 </mn> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> n </mi> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mrow> <mn> 1 </mn> <mo> , </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> ❘ </mo> <mtable> <mtr> <mtd> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 1 </mn> <mo> , </mo> <mo> … </mo> <mo> , </mo> <mn> 1 </mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 0 </mn> <mo> , </mo> <mo> … </mo> <mo> , </mo> <mn> 0 </mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List[RowBox[List["n", "+", "1"]], ",", RowBox[List["n", "+", "1"]]]], RowBox[List["1", ",", RowBox[List["n", "+", "1"]]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["1", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox["1", MeijerG, Rule[Editable, True]], ",", "1", ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", "1"]]], List[RowBox[List[TagBox["1", MeijerG, Rule[Editable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, True]] </annotation> </semantics> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <mi> ζ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mn> 2 </mn> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> n </mi> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mrow> <mn> 1 </mn> <mo> , </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> ❘ </mo> <mtable> <mtr> <mtd> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 1 </mn> <mo> , </mo> <mo> … </mo> <mo> , </mo> <mn> 1 </mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 0 </mn> <mo> , </mo> <mo> … </mo> <mo> , </mo> <mn> 0 </mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List[RowBox[List["n", "+", "1"]], ",", RowBox[List["n", "+", "1"]]]], RowBox[List["1", ",", RowBox[List["n", "+", "1"]]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["1", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox["1", MeijerG, Rule[Editable, True]], ",", "1", ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", "1"]]], List[RowBox[List[TagBox["1", MeijerG, Rule[Editable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, True]] </annotation> </semantics> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Zeta", "[", "n_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", ",", RowBox[List["1", "+", SubscriptBox["a", "1"]]], ",", "\[Ellipsis]", ",", RowBox[List["1", "+", SubscriptBox["a", "n"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "n"]]], "}"]]]], "}"]], ",", "1"]], "]"]], RowBox[List["1", "-", SuperscriptBox["2", RowBox[List["1", "-", "n"]]]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["a", "1"], "\[Equal]", SubscriptBox["a", "2"], "\[Equal]", "\[Ellipsis]", "\[Equal]", SubscriptBox["a", "n"], "\[Equal]", "0"]], "&&", RowBox[List[RowBox[List["n", "-", "1"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["n", "-", "1"]], ">", "0"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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