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variants of this functions
Zeta






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > Zeta[s] > Differentiation > Low-order differentiation > Derivatives at zero





http://functions.wolfram.com/10.01.20.0014.01









  


  










Input Form





Derivative[9][Zeta][0] == 4 EulerGamma^9 + (63/2) EulerGamma^8 Log[2 Pi] - (11813 Pi^8 Log[2 Pi])/2560 - (1/2) Log[2 Pi]^9 + 36 Log[2 Pi]^7 StieltjesGamma[1] + 9 EulerGamma^7 (Pi^2 + 4 (3 Log[2 Pi]^2 + StieltjesGamma[1])) + 126 Log[2 Pi]^6 StieltjesGamma[2] + 252 Log[2 Pi]^5 StieltjesGamma[3] + 315 Log[2 Pi]^4 StieltjesGamma[4] + 252 Log[2 Pi]^3 StieltjesGamma[5] + 126 Log[2 Pi]^2 StieltjesGamma[6] + 36 Log[2 Pi] StieltjesGamma[7] + (9 StieltjesGamma[8])/2 - 84 Log[2 Pi]^6 Zeta[3] + 2520 Log[2 Pi]^4 StieltjesGamma[1] Zeta[3] + 5040 Log[2 Pi]^3 StieltjesGamma[2] Zeta[3] + 5040 Log[2 Pi]^2 StieltjesGamma[3] Zeta[3] + 2520 Log[2 Pi] StieltjesGamma[4] Zeta[3] + 504 StieltjesGamma[5] Zeta[3] - 1680 Log[2 Pi]^3 Zeta[3]^2 + 10080 Log[2 Pi] StieltjesGamma[1] Zeta[3]^2 + 5040 StieltjesGamma[2] Zeta[3]^2 - 1120 Zeta[3]^3 - (275/32) Pi^6 (Log[2 Pi]^3 - 6 Log[2 Pi] StieltjesGamma[1] - 3 StieltjesGamma[2] + 2 Zeta[3]) + (21/2) EulerGamma^6 (5 Pi^2 Log[2 Pi] + 4 (5 Log[2 Pi]^3 + 6 Log[2 Pi] StieltjesGamma[1] + 3 StieltjesGamma[2] + 10 Zeta[3])) + (21/20) EulerGamma^5 (19 Pi^4 + 60 Pi^2 (2 Log[2 Pi]^2 + StieltjesGamma[1]) + 240 (Log[2 Pi]^4 + 3 Log[2 Pi]^2 StieltjesGamma[1] + 3 Log[2 Pi] StieltjesGamma[2] + StieltjesGamma[3] + 8 Log[2 Pi] Zeta[3])) - 1512 Log[2 Pi]^4 Zeta[5] + 18144 Log[2 Pi]^2 StieltjesGamma[1] Zeta[5] + 18144 Log[2 Pi] StieltjesGamma[2] Zeta[5] + 6048 StieltjesGamma[3] Zeta[5] - 12096 Log[2 Pi] Zeta[3] Zeta[5] - (399/80) Pi^4 (Log[2 Pi]^5 - 30 Log[2 Pi]^2 StieltjesGamma[2] - 20 Log[2 Pi] StieltjesGamma[3] - 5 StieltjesGamma[4] + 20 Log[2 Pi]^2 Zeta[3] - 20 StieltjesGamma[1] (Log[2 Pi]^3 + 2 Zeta[3]) + 24 Zeta[5]) + (63/16) EulerGamma^4 (19 Pi^4 Log[2 Pi] + 40 Pi^2 (Log[2 Pi]^3 + 2 Log[2 Pi] StieltjesGamma[1] + StieltjesGamma[2] + 2 Zeta[3]) + 16 (3 Log[2 Pi]^5 + 30 Log[2 Pi]^2 StieltjesGamma[2] + 20 Log[2 Pi] StieltjesGamma[3] + 5 StieltjesGamma[4] + 60 Log[2 Pi]^2 Zeta[3] + 20 StieltjesGamma[1] (Log[2 Pi]^3 + 2 Zeta[3]) + 72 Zeta[5])) + (1/16) EulerGamma^3 (275 Pi^6 + 1596 Pi^4 (Log[2 Pi]^2 + StieltjesGamma[1]) + 1680 Pi^2 (Log[2 Pi]^4 + 6 Log[2 Pi]^2 StieltjesGamma[1] + 6 Log[2 Pi] StieltjesGamma[2] + 2 StieltjesGamma[3] + 8 Log[2 Pi] Zeta[3]) + 1344 (Log[2 Pi]^6 + 30 Log[2 Pi]^2 StieltjesGamma[3] + 15 Log[2 Pi] StieltjesGamma[4] + 3 StieltjesGamma[5] + 40 Log[2 Pi]^3 Zeta[3] + 40 Zeta[3]^2 + 30 StieltjesGamma[2] (Log[2 Pi]^3 + 2 Zeta[3]) + 15 StieltjesGamma[1] (Log[2 Pi]^4 + 8 Log[2 Pi] Zeta[3]) + 144 Log[2 Pi] Zeta[5])) + (3/16) EulerGamma (275 Pi^6 StieltjesGamma[1] + 532 Pi^4 (3 Log[2 Pi]^2 StieltjesGamma[1] + 3 Log[2 Pi] StieltjesGamma[2] + StieltjesGamma[3]) + 336 Pi^2 (10 Log[2 Pi]^2 StieltjesGamma[3] + 5 Log[2 Pi] StieltjesGamma[4] + StieltjesGamma[5] + 10 StieltjesGamma[2] (Log[2 Pi]^3 + 2 Zeta[3]) + 5 StieltjesGamma[1] (Log[2 Pi]^4 + 8 Log[2 Pi] Zeta[3])) + 192 (35 Log[2 Pi]^4 StieltjesGamma[3] + 35 Log[2 Pi]^3 StieltjesGamma[4] + 21 Log[2 Pi]^2 StieltjesGamma[5] + 7 Log[2 Pi] StieltjesGamma[6] + StieltjesGamma[7] + 280 Log[2 Pi] StieltjesGamma[3] Zeta[3] + 70 StieltjesGamma[4] Zeta[3] + 21 StieltjesGamma[2] (Log[2 Pi]^5 + 20 Log[2 Pi]^2 Zeta[3] + 24 Zeta[5]) + 7 StieltjesGamma[1] (Log[2 Pi]^6 + 40 Log[2 Pi]^3 Zeta[3] + 40 Zeta[3]^2 + 144 Log[2 Pi] Zeta[5]))) - 12960 Log[2 Pi]^2 Zeta[7] + 25920 StieltjesGamma[1] Zeta[7] - (3/2) Pi^2 (Log[2 Pi]^7 - 140 Log[2 Pi]^3 StieltjesGamma[3] - 105 Log[2 Pi]^2 StieltjesGamma[4] - 42 Log[2 Pi] StieltjesGamma[5] - 7 StieltjesGamma[6] + 70 Log[2 Pi]^4 Zeta[3] - 280 StieltjesGamma[3] Zeta[3] + 280 Log[2 Pi] Zeta[3]^2 - 105 StieltjesGamma[2] (Log[2 Pi]^4 + 8 Log[2 Pi] Zeta[3]) + 504 Log[2 Pi]^2 Zeta[5] - 42 StieltjesGamma[1] (Log[2 Pi]^5 + 20 Log[2 Pi]^2 Zeta[3] + 24 Zeta[5]) + 720 Zeta[7]) + (3/32) EulerGamma^2 (275 Pi^6 Log[2 Pi] + 532 Pi^4 (Log[2 Pi]^3 + 6 Log[2 Pi] StieltjesGamma[1] + 3 StieltjesGamma[2] + 2 Zeta[3]) + 336 Pi^2 (Log[2 Pi]^5 + 30 Log[2 Pi]^2 StieltjesGamma[2] + 20 Log[2 Pi] StieltjesGamma[3] + 5 StieltjesGamma[4] + 20 Log[2 Pi]^2 Zeta[3] + 20 StieltjesGamma[1] (Log[2 Pi]^3 + 2 Zeta[3]) + 24 Zeta[5]) + 192 (Log[2 Pi]^7 + 140 Log[2 Pi]^3 StieltjesGamma[3] + 105 Log[2 Pi]^2 StieltjesGamma[4] + 42 Log[2 Pi] StieltjesGamma[5] + 7 StieltjesGamma[6] + 70 Log[2 Pi]^4 Zeta[3] + 280 StieltjesGamma[3] Zeta[3] + 280 Log[2 Pi] Zeta[3]^2 + 105 StieltjesGamma[2] (Log[2 Pi]^4 + 8 Log[2 Pi] Zeta[3]) + 504 Log[2 Pi]^2 Zeta[5] + 42 StieltjesGamma[1] (Log[2 Pi]^5 + 20 Log[2 Pi]^2 Zeta[3] + 24 Zeta[5]) + 720 Zeta[7])) - 20160 Zeta[9]










Standard Form





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TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, TagBox[&quot;3&quot;, Zeta, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <msup> <mi> log </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 21 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <msup> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> <mn> 6 </mn> </msup> <mo> &#8290; </mo> 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<mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 3 </mn> </msub> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, TagBox[&quot;3&quot;, Zeta, Rule[Editable, 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InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 24 </mn> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 5 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, TagBox[&quot;5&quot;, Zeta, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 280 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( 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</mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 42 </mn> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> log </mi> <mn> 5 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 20 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, TagBox[&quot;3&quot;, Zeta, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 24 </mn> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 5 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, TagBox[&quot;5&quot;, Zeta, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 1 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 140 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 3 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 105 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 4 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 42 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 5 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 6 </mn> </msub> </mrow> <mo> 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<mrow> <mn> 105 </mn> <mo> &#8290; </mo> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> log </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, TagBox[&quot;3&quot;, Zeta, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 280 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, TagBox[&quot;3&quot;, Zeta, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 280 </mn> <mo> &#8290; </mo> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, TagBox[&quot;3&quot;, Zeta, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 70 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, TagBox[&quot;3&quot;, Zeta, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <msup> <mi> log </mi> <mn> 7 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + 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</semantics> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, TagBox[&quot;3&quot;, Zeta, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <msup> <mi> log </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 336 </mn> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 20 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> log </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) 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<mo> ( </mo> <mrow> <mrow> <msup> <mi> log </mi> <mn> 5 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 20 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, TagBox[&quot;3&quot;, Zeta, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 24 </mn> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 5 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, 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TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, TagBox[&quot;7&quot;, Zeta, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 504 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 5 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, TagBox[&quot;5&quot;, Zeta, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 105 </mn> <mo> &#8290; </mo> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 2 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</mrow> <mo> + </mo> <mrow> <mn> 70 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, TagBox[&quot;3&quot;, Zeta, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <msup> <mi> log </mi> <mn> 7 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 275 </mn> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 6 </mn> </msup> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> 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</apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Zeta </ci> <cn type='integer'> 5 </cn> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 10080 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <apply> <power /> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2520 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 36 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 7 </cn> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <eulergamma /> <cn type='integer'> 7 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 1 </cn> </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> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 126 </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'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 252 </cn> 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type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 36 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 8 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 275 <sep /> 32 </cn> <apply> <power /> <pi /> <cn type='integer'> 6 </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'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <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'> 3 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 21 <sep /> 2 </cn> <apply> <power /> <eulergamma /> <cn type='integer'> 6 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <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'> 10 </cn> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <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='rational'> 21 <sep /> 20 </cn> <apply> <power /> <eulergamma /> <cn type='integer'> 5 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 60 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> 2 </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'> 240 </cn> <apply> <plus /> <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> <ci> StieltjesGamma </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </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> <ci> StieltjesGamma </ci> <cn type='integer'> 3 </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> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 4 </cn> </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'> 399 <sep /> 80 </cn> <apply> <power /> <pi /> <cn type='integer'> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -20 </cn> <apply> <plus /> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <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'> 30 </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'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 20 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </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'> 5 </cn> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 24 </cn> <apply> <ci> Zeta </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 20 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 2 </cn> </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'> 5 </cn> 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type='integer'> 4 </cn> </apply> <apply> <plus /> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1680 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 6 </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'> 6 </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'> 2 </cn> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 3 </cn> </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> <times /> <cn type='integer'> 1344 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 15 </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'> 30 </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> <times /> <cn type='integer'> 15 </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> <times /> <cn type='integer'> 3 </cn> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 144 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <apply> <ci> Zeta </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 30 </cn> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 40 </cn> <apply> <power /> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 40 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 3 </cn> </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'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 275 </cn> <apply> <power /> <pi /> <cn type='integer'> 6 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 3 <sep /> 16 </cn> <eulergamma /> <apply> <plus /> <apply> <times /> <cn type='integer'> 275 </cn> <apply> <power /> <pi /> <cn type='integer'> 6 </cn> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 532 </cn> <apply> <power /> <pi /> <cn type='integer'> 4 </cn> </apply> <apply> <plus /> <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> <ci> StieltjesGamma </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </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> <ci> StieltjesGamma </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 336 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </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'> 10 </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> <times /> <cn type='integer'> 5 </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> <ci> 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Rule Form





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





2007-05-02





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