Riemann zeta function: Differentiation (formula 10.01.20.0013)

Zeta

$Mathematica Notation$

Zeta Functions and Polylogarithms

Zeta[s]

Differentiation

Low-order differentiation

Derivatives at zero

http://functions.wolfram.com/10.01.20.0013.01

Input Form

Derivative[8][Zeta][0] == (7 EulerGamma^8)/2 - (11813 Pi^8)/23040 + 24 EulerGamma^7 Log[2 Pi] - (1/2) Log[2 Pi]^8 - (275/96) Pi^6 (Log[2 Pi]^2 - 2 StieltjesGamma[1]) + 28 Log[2 Pi]^6 StieltjesGamma[1] + (7/6) EulerGamma^6 (5 Pi^2 + 60 Log[2 Pi]^2 + 24 StieltjesGamma[1]) + 84 Log[2 Pi]^5 StieltjesGamma[2] + 140 Log[2 Pi]^4 StieltjesGamma[3] + 140 Log[2 Pi]^3 StieltjesGamma[4] + 84 Log[2 Pi]^2 StieltjesGamma[5] + 28 Log[2 Pi] StieltjesGamma[6] + 4 StieltjesGamma[7] - 56 Log[2 Pi]^5 Zeta[3] + 1120 Log[2 Pi]^3 StieltjesGamma[1] Zeta[3] + 1680 Log[2 Pi]^2 StieltjesGamma[2] Zeta[3] + 1120 Log[2 Pi] StieltjesGamma[3] Zeta[3] + 280 StieltjesGamma[4] Zeta[3] - 560 Log[2 Pi]^2 Zeta[3]^2 + 1120 StieltjesGamma[1] Zeta[3]^2 + 28 EulerGamma^5 (Pi^2 Log[2 Pi] + 4 Log[2 Pi]^3 + 6 Log[2 Pi] StieltjesGamma[1] + 3 StieltjesGamma[2] + 8 Zeta[3]) - (133/48) Pi^4 (Log[2 Pi]^4 - 12 Log[2 Pi]^2 StieltjesGamma[1] - 12 Log[2 Pi] StieltjesGamma[2] - 4 StieltjesGamma[3] + 8 Log[2 Pi] Zeta[3]) + (7/16) EulerGamma^4 (19 Pi^4 + 40 Pi^2 (3 Log[2 Pi]^2 + 2 StieltjesGamma[1]) + 80 (3 Log[2 Pi]^4 + 12 Log[2 Pi]^2 StieltjesGamma[1] + 12 Log[2 Pi] StieltjesGamma[2] + 4 StieltjesGamma[3] + 24 Log[2 Pi] Zeta[3])) - 672 Log[2 Pi]^3 Zeta[5] + 4032 Log[2 Pi] StieltjesGamma[1] Zeta[5] + 2016 StieltjesGamma[2] Zeta[5] - 1344 Zeta[3] Zeta[5] - (7/6) Pi^2 (Log[2 Pi]^6 - 60 Log[2 Pi]^2 StieltjesGamma[3] - 30 Log[2 Pi] StieltjesGamma[4] - 6 StieltjesGamma[5] + 40 Log[2 Pi]^3 Zeta[3] + 40 Zeta[3]^2 - 60 StieltjesGamma[2] (Log[2 Pi]^3 + 2 Zeta[3]) - 30 StieltjesGamma[1] (Log[2 Pi]^4 + 8 Log[2 Pi] Zeta[3]) + 144 Log[2 Pi] Zeta[5]) + (7/6) EulerGamma^3 (19 Pi^4 Log[2 Pi] + 20 Pi^2 (2 Log[2 Pi]^3 + 6 Log[2 Pi] StieltjesGamma[1] + 3 StieltjesGamma[2] + 4 Zeta[3]) + 24 (2 Log[2 Pi]^5 + 30 Log[2 Pi]^2 StieltjesGamma[2] + 20 Log[2 Pi] StieltjesGamma[3] + 5 StieltjesGamma[4] + 40 Log[2 Pi]^2 Zeta[3] + 20 StieltjesGamma[1] (Log[2 Pi]^3 + 2 Zeta[3]) + 48 Zeta[5])) + (1/96) EulerGamma^2 (275 Pi^6 + 1596 Pi^4 (Log[2 Pi]^2 + 2 StieltjesGamma[1]) + 1680 Pi^2 (Log[2 Pi]^4 + 12 Log[2 Pi]^2 StieltjesGamma[1] + 12 Log[2 Pi] StieltjesGamma[2] + 4 StieltjesGamma[3] + 8 Log[2 Pi] Zeta[3]) + 1344 (Log[2 Pi]^6 + 60 Log[2 Pi]^2 StieltjesGamma[3] + 30 Log[2 Pi] StieltjesGamma[4] + 6 StieltjesGamma[5] + 40 Log[2 Pi]^3 Zeta[3] + 40 Zeta[3]^2 + 60 StieltjesGamma[2] (Log[2 Pi]^3 + 2 Zeta[3]) + 30 StieltjesGamma[1] (Log[2 Pi]^4 + 8 Log[2 Pi] Zeta[3]) + 144 Log[2 Pi] Zeta[5])) + (7/4) EulerGamma (19 Pi^4 (2 Log[2 Pi] StieltjesGamma[1] + StieltjesGamma[2]) + 20 Pi^2 (6 Log[2 Pi]^2 StieltjesGamma[2] + 4 Log[2 Pi] StieltjesGamma[3] + StieltjesGamma[4] + 4 StieltjesGamma[1] (Log[2 Pi]^3 + 2 Zeta[3])) + 16 (20 Log[2 Pi]^3 StieltjesGamma[3] + 15 Log[2 Pi]^2 StieltjesGamma[4] + 6 Log[2 Pi] StieltjesGamma[5] + StieltjesGamma[6] + 40 StieltjesGamma[3] Zeta[3] + 15 StieltjesGamma[2] (Log[2 Pi]^4 + 8 Log[2 Pi] Zeta[3]) + 6 StieltjesGamma[1] (Log[2 Pi]^5 + 20 Log[2 Pi]^2 Zeta[3] + 24 Zeta[5]))) - 2880 Log[2 Pi] Zeta[7]

Standard Form

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MathML Form

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<mrow> <mn> 28 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 6 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 7 </mn> <mn> 6 </mn> </mfrac> <mo> ⁢ </mo> <msup> <semantics> <mi> ℽ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubledGamma]", Function[List[], EulerGamma]] </annotation> </semantics> <mn> 6 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 24 </mn> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 60 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 84 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 5 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 140 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 140 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 4 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 84 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 5 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 28 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 6 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 7 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 28 </mn> <mo> ⁢ </mo> <msup> <semantics> <mi> ℽ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubledGamma]", Function[List[], EulerGamma]] </annotation> </semantics> <mn> 5 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 133 </mn> <mn> 48 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 4 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 12 </mn> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 1 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 2 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <msup> <mi> log </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 7 </mn> <mn> 16 </mn> </mfrac> <mo> ⁢ </mo> <msup> <semantics> <mi> ℽ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubledGamma]", Function[List[], EulerGamma]] </annotation> </semantics> <mn> 4 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 40 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 80 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 24 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 19 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 4 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 7 </mn> <mn> 6 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 30 </mn> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> log </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 1 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 60 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 3 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 30 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 4 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 5 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 144 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 5 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["5", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> - </mo> <mrow> <mn> 60 </mn> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> log </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 40 </mn> <mo> ⁢ </mo> <msup> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 40 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <msup> <mi> log </mi> <mn> 6 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 7 </mn> <mn> 6 </mn> </mfrac> <mo> ⁢ </mo> <msup> <semantics> <mi> ℽ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubledGamma]", Function[List[], EulerGamma]] </annotation> </semantics> <mn> 3 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 20 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 24 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 20 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> log </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 30 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 20 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 4 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 48 </mn> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 5 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["5", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 40 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 5 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 19 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 4 </mn> </msup> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 96 </mn> </mfrac> <mo> ⁢ </mo> <msup> <semantics> <mi> ℽ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubledGamma]", Function[List[], EulerGamma]] </annotation> </semantics> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1596 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 4 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 1680 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <msup> <mi> log </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 1344 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 30 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> log </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 60 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 30 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 4 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 5 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 144 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 5 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["5", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 60 </mn> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> log </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 40 </mn> <mo> ⁢ </mo> <msup> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 40 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <msup> <mi> log </mi> <mn> 6 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 275 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 6 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 7 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <semantics> <mi> ℽ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubledGamma]", Function[List[], EulerGamma]] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 19 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 4 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 20 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> log </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 4 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> log </mi> <mn> 5 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 20 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 24 </mn> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 5 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["5", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 20 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 4 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 5 </mn> </msub> </mrow> <mo> + </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 6 </mn> </msub> <mo> + </mo> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> log </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 40 </mn> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 3 </mn> </msub> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2880 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <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]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 4032 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 5 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["5", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 2016 </mn> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 5 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["5", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> - </mo> <mrow> <mn> 1344 </mn> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 5 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["5", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> - </mo> <mrow> <mn> 672 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 5 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["5", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 1120 </mn> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msup> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 560 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1120 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 1680 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 1120 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 3 </mn> </msub> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 280 </mn> <mo> ⁢ </mo> <msub> <semantics> <mi> γ </mi> <annotation encoding='Mathematica'> TagBox["\[Gamma]", StieltjesGamma] </annotation> </semantics> <mn> 4 </mn> </msub> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> - </mo> <mrow> <mn> 56 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 5 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", TagBox["3", Zeta, Rule[Editable, True]], ")"]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 8 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 24 </mn> <mo> ⁢ </mo> <msup> <semantics> <mi> ℽ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubledGamma]", Function[List[], EulerGamma]] </annotation> </semantics> <mn> 7 </mn> </msup> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mfrac> <mrow> <mn> 11813 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 8 </mn> </msup> </mrow> <mn> 23040 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <msup> <semantics> <mi> ℽ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubledGamma]", Function[List[], EulerGamma]] </annotation> </semantics> <mn> 8 </mn> </msup> </mrow> <mn> 2 </mn> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> D </ci> <apply> <ci> Zeta </ci> <cn type='integer'> 0 </cn> </apply> <list> <cn type='integer'> 0 </cn> <cn type='integer'> 8 </cn> </list> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 275 <sep /> 96 </cn> </apply> <apply> <power /> <pi /> <cn type='integer'> 6 </cn> </apply> <apply> <plus /> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 28 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 6 </cn> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 7 <sep /> 6 </cn> <apply> <power /> <eulergamma /> <cn type='integer'> 6 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 24 </cn> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 60 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 84 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 5 </cn> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 140 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 140 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 84 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 28 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 28 </cn> <apply> <power /> <eulergamma /> <cn type='integer'> 5 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 133 <sep /> 48 </cn> <apply> <power /> <pi /> <cn type='integer'> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -12 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 7 <sep /> 16 </cn> <apply> <power /> <eulergamma /> <cn type='integer'> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 40 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 80 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 24 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 19 </cn> <apply> <power /> <pi /> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 7 <sep /> 6 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -30 </cn> <apply> <plus /> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 60 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 30 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> 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Rule Form

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

2007-05-02

Zeta[s,a]