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http://functions.wolfram.com/10.01.03.0059.01
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Zeta[7] == ((2 Pi^6)/945) (Log[2 Pi] +
84 (720 PolyGamma[-8, 1] - 360 PolyGamma[-7, 1] + 60 PolyGamma[-6, 1] -
PolyGamma[-4, 1]))
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Cell[BoxData[RowBox[List[RowBox[List["Zeta", "[", "7", "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[Pi]", "6"]]], "945"], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["2", " ", "\[Pi]"]], "]"]], "+", RowBox[List["84", " ", RowBox[List["(", RowBox[List[RowBox[List["720", " ", RowBox[List["PolyGamma", "[", RowBox[List[RowBox[List["-", "8"]], ",", "1"]], "]"]]]], "-", RowBox[List["360", " ", RowBox[List["PolyGamma", "[", RowBox[List[RowBox[List["-", "7"]], ",", "1"]], "]"]]]], "+", RowBox[List["60", " ", RowBox[List["PolyGamma", "[", RowBox[List[RowBox[List["-", "6"]], ",", "1"]], "]"]]]], "-", RowBox[List["PolyGamma", "[", RowBox[List[RowBox[List["-", "4"]], ",", "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> 7 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["7", Zeta, Rule[Editable, True], Rule[Selectable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]], Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> <mo>  </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 6 </mn> </msup> </mrow> <mn> 945 </mn> </mfrac> <mo> ⁢ </mo> <mtext> </mtext> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 84 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 720 </mn> <mo> ⁢ </mo> <mrow> <msup> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 8 </mn> </mrow> <mo> ) </mo> </mrow> </msup> <mo> ( </mo> <mn> 1 </mn> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 360 </mn> <mo> ⁢ </mo> <mrow> <msup> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> </msup> <mo> ( </mo> <mn> 1 </mn> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 60 </mn> <mo> ⁢ </mo> <mrow> <msup> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> </msup> <mo> ( </mo> <mn> 1 </mn> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msup> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> </msup> <mo> ( </mo> <mn> 1 </mn> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Zeta </ci> <cn type='integer'> 7 </cn> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <pi /> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <cn type='integer'> 945 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <apply> <times /> <cn type='integer'> 84 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 720 </cn> <apply> <ci> PolyGamma </ci> <cn type='integer'> -8 </cn> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 360 </cn> <apply> <ci> PolyGamma </ci> <cn type='integer'> -7 </cn> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 60 </cn> <apply> <ci> PolyGamma </ci> <cn type='integer'> -6 </cn> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> PolyGamma </ci> <cn type='integer'> -4 </cn> <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", "[", "7", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "945"], " ", RowBox[List["(", RowBox[List["2", " ", SuperscriptBox["\[Pi]", "6"]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["2", " ", "\[Pi]"]], "]"]], "+", RowBox[List["84", " ", RowBox[List["(", RowBox[List[RowBox[List["720", " ", RowBox[List["PolyGamma", "[", RowBox[List[RowBox[List["-", "8"]], ",", "1"]], "]"]]]], "-", RowBox[List["360", " ", RowBox[List["PolyGamma", "[", RowBox[List[RowBox[List["-", "7"]], ",", "1"]], "]"]]]], "+", RowBox[List["60", " ", RowBox[List["PolyGamma", "[", RowBox[List[RowBox[List["-", "6"]], ",", "1"]], "]"]]]], "-", RowBox[List["PolyGamma", "[", RowBox[List[RowBox[List["-", "4"]], ",", "1"]], "]"]]]], ")"]]]]]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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