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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/10.01.20.0017.01









  


  










Input Form





Derivative[12][Zeta][0] == (11 EulerGamma^12)/2 - (193814931 Pi^12)/3727360 + 60 EulerGamma^11 Log[2 Pi] - (1/2) Log[2 Pi]^12 - (285795 Pi^10 (Log[2 Pi]^2 - 2 StieltjesGamma[1]))/1024 + 66 Log[2 Pi]^10 StieltjesGamma[1] + (33/4) EulerGamma^10 (3 Pi^2 + 36 Log[2 Pi]^2 + 8 StieltjesGamma[1]) + 330 Log[2 Pi]^9 StieltjesGamma[2] + 990 Log[2 Pi]^8 StieltjesGamma[3] + 1980 Log[2 Pi]^7 StieltjesGamma[4] + 2772 Log[2 Pi]^6 StieltjesGamma[5] + 2772 Log[2 Pi]^5 StieltjesGamma[6] + 1980 Log[2 Pi]^4 StieltjesGamma[7] + 990 Log[2 Pi]^3 StieltjesGamma[8] + 330 Log[2 Pi]^2 StieltjesGamma[9] + 66 Log[2 Pi] StieltjesGamma[10] + 6 StieltjesGamma[11] - 220 Log[2 Pi]^9 Zeta[3] + 15840 Log[2 Pi]^7 StieltjesGamma[1] Zeta[3] + 55440 Log[2 Pi]^6 StieltjesGamma[2] Zeta[3] + 110880 Log[2 Pi]^5 StieltjesGamma[3] Zeta[3] + 138600 Log[2 Pi]^4 StieltjesGamma[4] Zeta[3] + 110880 Log[2 Pi]^3 StieltjesGamma[5] Zeta[3] + 55440 Log[2 Pi]^2 StieltjesGamma[6] Zeta[3] + 15840 Log[2 Pi] StieltjesGamma[7] Zeta[3] + 1980 StieltjesGamma[8] Zeta[3] - 18480 Log[2 Pi]^6 Zeta[3]^2 + 554400 Log[2 Pi]^4 StieltjesGamma[1] Zeta[3]^2 + 1108800 Log[2 Pi]^3 StieltjesGamma[2] Zeta[3]^2 + 1108800 Log[2 Pi]^2 StieltjesGamma[3] Zeta[3]^2 + 554400 Log[2 Pi] StieltjesGamma[4] Zeta[3]^2 + 110880 StieltjesGamma[5] Zeta[3]^2 - 246400 Log[2 Pi]^3 Zeta[3]^3 + 1478400 Log[2 Pi] StieltjesGamma[1] Zeta[3]^3 + 739200 StieltjesGamma[2] Zeta[3]^3 - 123200 Zeta[3]^4 + 110 EulerGamma^9 (2 Pi^2 Log[2 Pi] + 8 Log[2 Pi]^3 + 6 Log[2 Pi] StieltjesGamma[1] + 3 StieltjesGamma[2] + 16 Zeta[3]) - (129943/512) Pi^8 (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]) + (33/32) EulerGamma^8 (133 Pi^4 + 120 Pi^2 (7 Log[2 Pi]^2 + 2 StieltjesGamma[1]) + 240 (7 Log[2 Pi]^4 + 12 Log[2 Pi]^2 StieltjesGamma[1] + 12 Log[2 Pi] StieltjesGamma[2] + 4 StieltjesGamma[3] + 56 Log[2 Pi] Zeta[3])) - 9504 Log[2 Pi]^7 Zeta[5] + 399168 Log[2 Pi]^5 StieltjesGamma[1] Zeta[5] + 997920 Log[2 Pi]^4 StieltjesGamma[2] Zeta[5] + 1330560 Log[2 Pi]^3 StieltjesGamma[3] Zeta[5] + 997920 Log[2 Pi]^2 StieltjesGamma[4] Zeta[5] + 399168 Log[2 Pi] StieltjesGamma[5] Zeta[5] + 66528 StieltjesGamma[6] Zeta[5] - 665280 Log[2 Pi]^4 Zeta[3] Zeta[5] + 7983360 Log[2 Pi]^2 StieltjesGamma[1] Zeta[3] Zeta[5] + 7983360 Log[2 Pi] StieltjesGamma[2] Zeta[3] Zeta[5] + 2661120 StieltjesGamma[3] Zeta[3] Zeta[5] - 2661120 Log[2 Pi] Zeta[3]^2 Zeta[5] - 2395008 Log[2 Pi]^2 Zeta[5]^2 + 4790016 StieltjesGamma[1] Zeta[5]^2 - (3025/32) Pi^6 (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]) + (99/2) EulerGamma^7 (19 Pi^4 Log[2 Pi] + 20 Pi^2 (2 Log[2 Pi]^3 + 2 Log[2 Pi] StieltjesGamma[1] + StieltjesGamma[2] + 4 Zeta[3]) + 8 (6 Log[2 Pi]^5 + 30 Log[2 Pi]^2 StieltjesGamma[2] + 20 Log[2 Pi] StieltjesGamma[3] + 5 StieltjesGamma[4] + 120 Log[2 Pi]^2 Zeta[3] + 20 StieltjesGamma[1] (Log[2 Pi]^3 + 2 Zeta[3]) + 144 Zeta[5])) + (11/32) EulerGamma^6 (1375 Pi^6 + 1596 Pi^4 (5 Log[2 Pi]^2 + 2 StieltjesGamma[1]) + 1680 Pi^2 (5 Log[2 Pi]^4 + 12 Log[2 Pi]^2 StieltjesGamma[1] + 12 Log[2 Pi] StieltjesGamma[2] + 4 StieltjesGamma[3] + 40 Log[2 Pi] Zeta[3]) + 1344 (5 Log[2 Pi]^6 + 60 Log[2 Pi]^2 StieltjesGamma[3] + 30 Log[2 Pi] StieltjesGamma[4] + 6 StieltjesGamma[5] + 200 Log[2 Pi]^3 Zeta[3] + 200 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]) + 720 Log[2 Pi] Zeta[5])) - 285120 Log[2 Pi]^5 Zeta[7] + 5702400 Log[2 Pi]^3 StieltjesGamma[1] Zeta[7] + 8553600 Log[2 Pi]^2 StieltjesGamma[2] Zeta[7] + 5702400 Log[2 Pi] StieltjesGamma[3] Zeta[7] + 1425600 StieltjesGamma[4] Zeta[7] - 5702400 Log[2 Pi]^2 Zeta[3] Zeta[7] + 11404800 StieltjesGamma[1] Zeta[3] Zeta[7] - 6842880 Zeta[5] Zeta[7] - (627/32) Pi^4 (Log[2 Pi]^8 - 280 Log[2 Pi]^4 StieltjesGamma[3] - 280 Log[2 Pi]^3 StieltjesGamma[4] - 168 Log[2 Pi]^2 StieltjesGamma[5] - 56 Log[2 Pi] StieltjesGamma[6] - 8 StieltjesGamma[7] + 112 Log[2 Pi]^5 Zeta[3] - 2240 Log[2 Pi] StieltjesGamma[3] Zeta[3] - 560 StieltjesGamma[4] Zeta[3] + 1120 Log[2 Pi]^2 Zeta[3]^2 + 1344 Log[2 Pi]^3 Zeta[5] + 2688 Zeta[3] Zeta[5] - 168 StieltjesGamma[2] (Log[2 Pi]^5 + 20 Log[2 Pi]^2 Zeta[3] + 24 Zeta[5]) - 56 StieltjesGamma[1] (Log[2 Pi]^6 + 40 Log[2 Pi]^3 Zeta[3] + 40 Zeta[3]^2 + 144 Log[2 Pi] Zeta[5]) + 5760 Log[2 Pi] Zeta[7]) + (33/4) EulerGamma^5 (275 Pi^6 Log[2 Pi] + 133 Pi^4 (4 Log[2 Pi]^3 + 6 Log[2 Pi] StieltjesGamma[1] + 3 StieltjesGamma[2] + 8 Zeta[3]) + 84 Pi^2 (4 Log[2 Pi]^5 + 30 Log[2 Pi]^2 StieltjesGamma[2] + 20 Log[2 Pi] StieltjesGamma[3] + 5 StieltjesGamma[4] + 80 Log[2 Pi]^2 Zeta[3] + 20 StieltjesGamma[1] (Log[2 Pi]^3 + 2 Zeta[3]) + 96 Zeta[5]) + 48 (4 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] + 280 Log[2 Pi]^4 Zeta[3] + 280 StieltjesGamma[3] Zeta[3] + 1120 Log[2 Pi] Zeta[3]^2 + 105 StieltjesGamma[2] (Log[2 Pi]^4 + 8 Log[2 Pi] Zeta[3]) + 2016 Log[2 Pi]^2 Zeta[5] + 42 StieltjesGamma[1] (Log[2 Pi]^5 + 20 Log[2 Pi]^2 Zeta[3] + 24 Zeta[5]) + 2880 Zeta[7])) + (33/512) EulerGamma^4 (11813 Pi^8 + 22000 Pi^6 (3 Log[2 Pi]^2 + 2 StieltjesGamma[1]) + 21280 Pi^4 (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]) + 26880 Pi^2 (Log[2 Pi]^6 + 20 Log[2 Pi]^2 StieltjesGamma[3] + 10 Log[2 Pi] StieltjesGamma[4] + 2 StieltjesGamma[5] + 40 Log[2 Pi]^3 Zeta[3] + 40 Zeta[3]^2 + 20 StieltjesGamma[2] (Log[2 Pi]^3 + 2 Zeta[3]) + 10 StieltjesGamma[1] (Log[2 Pi]^4 + 8 Log[2 Pi] Zeta[3]) + 144 Log[2 Pi] Zeta[5]) + 3840 (3 Log[2 Pi]^8 + 280 Log[2 Pi]^4 StieltjesGamma[3] + 280 Log[2 Pi]^3 StieltjesGamma[4] + 168 Log[2 Pi]^2 StieltjesGamma[5] + 56 Log[2 Pi] StieltjesGamma[6] + 8 StieltjesGamma[7] + 336 Log[2 Pi]^5 Zeta[3] + 2240 Log[2 Pi] StieltjesGamma[3] Zeta[3] + 560 StieltjesGamma[4] Zeta[3] + 3360 Log[2 Pi]^2 Zeta[3]^2 + 4032 Log[2 Pi]^3 Zeta[5] + 8064 Zeta[3] Zeta[5] + 168 StieltjesGamma[2] (Log[2 Pi]^5 + 20 Log[2 Pi]^2 Zeta[3] + 24 Zeta[5]) + 56 StieltjesGamma[1] (Log[2 Pi]^6 + 40 Log[2 Pi]^3 Zeta[3] + 40 Zeta[3]^2 + 144 Log[2 Pi] Zeta[5]) + 17280 Log[2 Pi] Zeta[7])) - 4435200 Log[2 Pi]^3 Zeta[9] + 26611200 Log[2 Pi] StieltjesGamma[1] Zeta[9] + 13305600 StieltjesGamma[2] Zeta[9] - 8870400 Zeta[3] Zeta[9] - (11/4) Pi^2 (Log[2 Pi]^10 - 840 Log[2 Pi]^6 StieltjesGamma[3] - 1260 Log[2 Pi]^5 StieltjesGamma[4] - 1260 Log[2 Pi]^4 StieltjesGamma[5] - 840 Log[2 Pi]^3 StieltjesGamma[6] - 360 Log[2 Pi]^2 StieltjesGamma[7] - 90 Log[2 Pi] StieltjesGamma[8] - 10 StieltjesGamma[9] + 240 Log[2 Pi]^7 Zeta[3] - 33600 Log[2 Pi]^3 StieltjesGamma[3] Zeta[3] - 25200 Log[2 Pi]^2 StieltjesGamma[4] Zeta[3] - 10080 Log[2 Pi] StieltjesGamma[5] Zeta[3] - 1680 StieltjesGamma[6] Zeta[3] + 8400 Log[2 Pi]^4 Zeta[3]^2 - 33600 StieltjesGamma[3] Zeta[3]^2 + 22400 Log[2 Pi] Zeta[3]^3 + 6048 Log[2 Pi]^5 Zeta[5] - 120960 Log[2 Pi] StieltjesGamma[3] Zeta[5] - 30240 StieltjesGamma[4] Zeta[5] + 120960 Log[2 Pi]^2 Zeta[3] Zeta[5] + 72576 Zeta[5]^2 + 86400 Log[2 Pi]^3 Zeta[7] + 172800 Zeta[3] Zeta[7] - 360 StieltjesGamma[2] (Log[2 Pi]^7 + 70 Log[2 Pi]^4 Zeta[3] + 280 Log[2 Pi] Zeta[3]^2 + 504 Log[2 Pi]^2 Zeta[5] + 720 Zeta[7]) - 90 StieltjesGamma[1] (Log[2 Pi]^8 + 112 Log[2 Pi]^5 Zeta[3] + 1120 Log[2 Pi]^2 Zeta[3]^2 + 1344 Log[2 Pi]^3 Zeta[5] + 2688 Zeta[3] Zeta[5] + 5760 Log[2 Pi] Zeta[7]) + 403200 Log[2 Pi] Zeta[9]) + (11/64) EulerGamma^3 (11813 Pi^8 Log[2 Pi] + 11000 Pi^6 (2 Log[2 Pi]^3 + 6 Log[2 Pi] StieltjesGamma[1] + 3 StieltjesGamma[2] + 4 Zeta[3]) + 6384 Pi^4 (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]) + 1920 Pi^2 (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] + 140 Log[2 Pi]^4 Zeta[3] + 280 StieltjesGamma[3] Zeta[3] + 560 Log[2 Pi] Zeta[3]^2 + 105 StieltjesGamma[2] (Log[2 Pi]^4 + 8 Log[2 Pi] Zeta[3]) + 1008 Log[2 Pi]^2 Zeta[5] + 42 StieltjesGamma[1] (Log[2 Pi]^5 + 20 Log[2 Pi]^2 Zeta[3] + 24 Zeta[5]) + 1440 Zeta[7]) + 640 (2 Log[2 Pi]^9 + 504 Log[2 Pi]^5 StieltjesGamma[3] + 630 Log[2 Pi]^4 StieltjesGamma[4] + 504 Log[2 Pi]^3 StieltjesGamma[5] + 252 Log[2 Pi]^2 StieltjesGamma[6] + 72 Log[2 Pi] StieltjesGamma[7] + 9 StieltjesGamma[8] + 336 Log[2 Pi]^6 Zeta[3] + 10080 Log[2 Pi]^2 StieltjesGamma[3] Zeta[3] + 5040 Log[2 Pi] StieltjesGamma[4] Zeta[3] + 1008 StieltjesGamma[5] Zeta[3] + 6720 Log[2 Pi]^3 Zeta[3]^2 + 4480 Zeta[3]^3 + 6048 Log[2 Pi]^4 Zeta[5] + 12096 StieltjesGamma[3] Zeta[5] + 48384 Log[2 Pi] Zeta[3] Zeta[5] + 252 StieltjesGamma[2] (Log[2 Pi]^6 + 40 Log[2 Pi]^3 Zeta[3] + 40 Zeta[3]^2 + 144 Log[2 Pi] Zeta[5]) + 51840 Log[2 Pi]^2 Zeta[7] + 72 StieltjesGamma[1] (Log[2 Pi]^7 + 70 Log[2 Pi]^4 Zeta[3] + 280 Log[2 Pi] Zeta[3]^2 + 504 Log[2 Pi]^2 Zeta[5] + 720 Zeta[7]) + 80640 Zeta[9])) + (1/1024) (3 EulerGamma^2 (95265 Pi^10 + 519772 Pi^8 (Log[2 Pi]^2 + 2 StieltjesGamma[1]) + 484000 Pi^6 (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]) + 187264 Pi^4 (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]) + 42240 Pi^2 (Log[2 Pi]^8 + 280 Log[2 Pi]^4 StieltjesGamma[3] + 280 Log[2 Pi]^3 StieltjesGamma[4] + 168 Log[2 Pi]^2 StieltjesGamma[5] + 56 Log[2 Pi] StieltjesGamma[6] + 8 StieltjesGamma[7] + 112 Log[2 Pi]^5 Zeta[3] + 2240 Log[2 Pi] StieltjesGamma[3] Zeta[3] + 560 StieltjesGamma[4] Zeta[3] + 1120 Log[2 Pi]^2 Zeta[3]^2 + 1344 Log[2 Pi]^3 Zeta[5] + 2688 Zeta[3] Zeta[5] + 168 StieltjesGamma[2] (Log[2 Pi]^5 + 20 Log[2 Pi]^2 Zeta[3] + 24 Zeta[5]) + 56 StieltjesGamma[1] (Log[2 Pi]^6 + 40 Log[2 Pi]^3 Zeta[3] + 40 Zeta[3]^2 + 144 Log[2 Pi] Zeta[5]) + 5760 Log[2 Pi] Zeta[7]) + 11264 (Log[2 Pi]^10 + 840 Log[2 Pi]^6 StieltjesGamma[3] + 1260 Log[2 Pi]^5 StieltjesGamma[4] + 1260 Log[2 Pi]^4 StieltjesGamma[5] + 840 Log[2 Pi]^3 StieltjesGamma[6] + 360 Log[2 Pi]^2 StieltjesGamma[7] + 90 Log[2 Pi] StieltjesGamma[8] + 10 StieltjesGamma[9] + 240 Log[2 Pi]^7 Zeta[3] + 33600 Log[2 Pi]^3 StieltjesGamma[3] Zeta[3] + 25200 Log[2 Pi]^2 StieltjesGamma[4] Zeta[3] + 10080 Log[2 Pi] StieltjesGamma[5] Zeta[3] + 1680 StieltjesGamma[6] Zeta[3] + 8400 Log[2 Pi]^4 Zeta[3]^2 + 33600 StieltjesGamma[3] Zeta[3]^2 + 22400 Log[2 Pi] Zeta[3]^3 + 6048 Log[2 Pi]^5 Zeta[5] + 120960 Log[2 Pi] StieltjesGamma[3] Zeta[5] + 30240 StieltjesGamma[4] Zeta[5] + 120960 Log[2 Pi]^2 Zeta[3] Zeta[5] + 72576 Zeta[5]^2 + 86400 Log[2 Pi]^3 Zeta[7] + 172800 Zeta[3] Zeta[7] + 360 StieltjesGamma[2] (Log[2 Pi]^7 + 70 Log[2 Pi]^4 Zeta[3] + 280 Log[2 Pi] Zeta[3]^2 + 504 Log[2 Pi]^2 Zeta[5] + 720 Zeta[7]) + 90 StieltjesGamma[1] (Log[2 Pi]^8 + 112 Log[2 Pi]^5 Zeta[3] + 1120 Log[2 Pi]^2 Zeta[3]^2 + 1344 Log[2 Pi]^3 Zeta[5] + 2688 Zeta[3] Zeta[5] + 5760 Log[2 Pi] Zeta[7]) + 403200 Log[2 Pi] Zeta[9]))) + (33/128) EulerGamma (11813 Pi^8 (2 Log[2 Pi] StieltjesGamma[1] + StieltjesGamma[2]) + 11000 Pi^6 (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])) + 4256 Pi^4 (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])) + 960 Pi^2 (56 Log[2 Pi]^5 StieltjesGamma[3] + 70 Log[2 Pi]^4 StieltjesGamma[4] + 56 Log[2 Pi]^3 StieltjesGamma[5] + 28 Log[2 Pi]^2 StieltjesGamma[6] + 8 Log[2 Pi] StieltjesGamma[7] + StieltjesGamma[8] + 1120 Log[2 Pi]^2 StieltjesGamma[3] Zeta[3] + 560 Log[2 Pi] StieltjesGamma[4] Zeta[3] + 112 StieltjesGamma[5] Zeta[3] + 1344 StieltjesGamma[3] Zeta[5] + 28 StieltjesGamma[2] (Log[2 Pi]^6 + 40 Log[2 Pi]^3 Zeta[3] + 40 Zeta[3]^2 + 144 Log[2 Pi] Zeta[5]) + 8 StieltjesGamma[1] (Log[2 Pi]^7 + 70 Log[2 Pi]^4 Zeta[3] + 280 Log[2 Pi] Zeta[3]^2 + 504 Log[2 Pi]^2 Zeta[5] + 720 Zeta[7])) + 256 (120 Log[2 Pi]^7 StieltjesGamma[3] + 210 Log[2 Pi]^6 StieltjesGamma[4] + 252 Log[2 Pi]^5 StieltjesGamma[5] + 210 Log[2 Pi]^4 StieltjesGamma[6] + 120 Log[2 Pi]^3 StieltjesGamma[7] + 45 Log[2 Pi]^2 StieltjesGamma[8] + 10 Log[2 Pi] StieltjesGamma[9] + StieltjesGamma[10] + 8400 Log[2 Pi]^4 StieltjesGamma[3] Zeta[3] + 8400 Log[2 Pi]^3 StieltjesGamma[4] Zeta[3] + 5040 Log[2 Pi]^2 StieltjesGamma[5] Zeta[3] + 1680 Log[2 Pi] StieltjesGamma[6] Zeta[3] + 240 StieltjesGamma[7] Zeta[3] + 33600 Log[2 Pi] StieltjesGamma[3] Zeta[3]^2 + 8400 StieltjesGamma[4] Zeta[3]^2 + 60480 Log[2 Pi]^2 StieltjesGamma[3] Zeta[5] + 30240 Log[2 Pi] StieltjesGamma[4] Zeta[5] + 6048 StieltjesGamma[5] Zeta[5] + 86400 StieltjesGamma[3] Zeta[7] + 45 StieltjesGamma[2] (Log[2 Pi]^8 + 112 Log[2 Pi]^5 Zeta[3] + 1120 Log[2 Pi]^2 Zeta[3]^2 + 1344 Log[2 Pi]^3 Zeta[5] + 2688 Zeta[3] Zeta[5] + 5760 Log[2 Pi] Zeta[7]) + 10 StieltjesGamma[1] (Log[2 Pi]^9 + 168 Log[2 Pi]^6 Zeta[3] + 3360 Log[2 Pi]^3 Zeta[3]^2 + 3024 Log[2 Pi]^4 Zeta[5] + 24192 Log[2 Pi] Zeta[3] Zeta[5] + 25920 Log[2 Pi]^2 Zeta[7] + 2240 (Zeta[3]^3 + 18 Zeta[9])))) - 21772800 Log[2 Pi] Zeta[11]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox["Zeta", TagBox[RowBox[List["(", "12", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "0", "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["11", " ", SuperscriptBox["EulerGamma", "12"]]], "2"], "-", FractionBox[RowBox[List["193814931", " ", SuperscriptBox["\[Pi]", "12"]]], "3727360"], "+", RowBox[List["60", " ", SuperscriptBox["EulerGamma", "11"], " ", RowBox[List["Log", "[", RowBox[List["2", " ", "\[Pi]"]], "]"]]]], "-", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox[RowBox[List["Log", "[", RowBox[List["2", " ", "\[Pi]"]], "]"]], "12"]]], "-", FractionBox[RowBox[List["285795", " ", SuperscriptBox["\[Pi]", "10"], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["Log", "[", RowBox[List["2", " ", "\[Pi]"]], "]"]], "2"], "-", RowBox[List["2", " ", RowBox[List["StieltjesGamma", "[", "1", "]"]]]]]], ")"]]]], "1024"], "+", RowBox[List["66", " ", SuperscriptBox[RowBox[List["Log", "[", RowBox[List["2", " ", 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encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 1 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 60 </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> 3 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 30 </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> 4 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <msub> <semantics> <mi> &#947; </mi> 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<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> </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> 30 </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> 2 </mn> </msub> 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</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> 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> + 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</mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 630 </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> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 4 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 504 </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> 5 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 252 </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> 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<semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <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> 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> <mo> + </mo> <mrow> <msup> <mi> log 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<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> <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> 1344 </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> <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, 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TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 8 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 9 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 403200 </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> 9 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, TagBox[&quot;9&quot;, Zeta, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 360 </mn> <mo> &#8290; </mo> <msub> <semantics> <mi> &#947; </mi> 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</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> 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> 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> 720 </mn> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 7 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> 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> </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> 56 </mn> <mo> &#8290; </mo> <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> &#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> 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> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 4 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 56 </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> 5 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 28 </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> 6 </mn> </msub> </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> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 7 </mn> </msub> </mrow> <mo> + </mo> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 8 </mn> </msub> <mo> + </mo> <mrow> <mn> 28 </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> 6 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 40 </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> <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> 40 </mn> <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> 144 </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> 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> 1344 </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> 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> 1120 </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> 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> 560 </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> 4 </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> 112 </mn> <mo> &#8290; </mo> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 5 </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;, 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InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 3360 </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> <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> 3024 </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> 5 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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> 25920 </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> 7 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> 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> 2240 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <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> 3 </mn> </msup> <mo> + </mo> <mrow> <mn> 18 </mn> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 9 </mn> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, TagBox[&quot;9&quot;, Zeta, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[BoxForm`e$, Zeta[BoxForm`e$]]]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> </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> 120 </mn> <mo> &#8290; </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> <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> 210 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 6 </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> 252 </mn> <mo> &#8290; </mo> <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> &#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> 210 </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> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 6 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 120 </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> 7 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 45 </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> 8 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 10 </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> 9 </mn> </msub> </mrow> <mo> + </mo> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 10 </mn> </msub> <mo> + </mo> <mrow> <mn> 45 </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> 8 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 112 </mn> <mo> &#8290; </mo> <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> &#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> 1120 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> 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<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> 123200 </mn> <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> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1478400 </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> 1 </mn> </msub> <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> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 739200 </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> <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> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 246400 </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> <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> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 554400 </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> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 1 </mn> </msub> <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> 1108800 </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> 2 </mn> </msub> <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> 1108800 </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> 3 </mn> </msub> <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> 554400 </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> 4 </mn> </msub> <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> 110880 </mn> <mo> &#8290; </mo> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 5 </mn> </msub> <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> 18480 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 6 </mn> </msup> <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> 15840 </mn> <mo> &#8290; </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> <mo> &#8290; </mo> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 1 </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> 55440 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 6 </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> 2 </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> 110880 </mn> <mo> &#8290; </mo> <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> &#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> 138600 </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> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 4 </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> 110880 </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> 5 </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> 55440 </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> 6 </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> 15840 </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> 7 </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> 1980 </mn> <mo> &#8290; </mo> <msub> <semantics> <mi> &#947; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Gamma]&quot;, StieltjesGamma] </annotation> </semantics> <mn> 8 </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> 220 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 9 </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> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 12 </mn> </msup> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 60 </mn> <mo> &#8290; </mo> <msup> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> <mn> 11 </mn> </msup> <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> </mrow> <mo> - </mo> <mfrac> <mrow> <mn> 193814931 </mn> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 12 </mn> </msup> </mrow> <mn> 3727360 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 11 </mn> <mo> &#8290; </mo> <msup> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> <mn> 12 </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 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</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> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 5 </cn> </apply> </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'> -1 </cn> <apply> <times 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</apply> <apply> <times /> <cn type='rational'> 99 <sep /> 2 </cn> <apply> <power /> <eulergamma /> <cn type='integer'> 7 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 20 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </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> <ci> StieltjesGamma </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> </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'> 3 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <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'> 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> <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> <times /> <cn type='integer'> 5 </cn> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 144 </cn> <apply> <ci> Zeta </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 120 </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> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 5 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 19 </cn> <apply> <power /> <pi /> <cn type='integer'> 4 </cn> </apply> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 11 <sep /> 32 </cn> <apply> <power /> <eulergamma /> <cn type='integer'> 6 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 1596 </cn> <apply> <power 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</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'> 40 </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'> 5 </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'> 1344 </cn> <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'> 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> <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> <times /> <cn type='integer'> 6 </cn> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 720 </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'> 60 </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'> 200 </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'> 200 </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> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 6 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1375 </cn> <apply> <power /> <pi /> <cn type='integer'> 6 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 627 <sep /> 32 </cn> <apply> <power /> <pi /> <cn type='integer'> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -56 </cn> <apply> <plus /> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 6 </cn> </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> <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'> 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> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 280 </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> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 280 </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> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 168 </cn> 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type='integer'> 560 </cn> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 336 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 5 </cn> </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'> 8 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 11813 </cn> <apply> <power /> <pi /> <cn type='integer'> 8 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 11 <sep /> 4 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 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type='integer'> 484000 </cn> <apply> <power /> <pi /> <cn type='integer'> 6 </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'> 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'> 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 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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> <times /> <cn type='integer'> 6 </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'> 60 </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 /> 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type='integer'> 5 </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'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 11264 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 90 </cn> <apply> <plus /> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 8 </cn> </apply> <apply> <times /> <cn type='integer'> 112 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 5 </cn> </apply> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1120 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1344 </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'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2688 </cn> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Zeta </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5760 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <apply> <ci> Zeta </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 840 </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'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1260 </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'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1260 </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'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 840 </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'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 360 </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'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 90 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 10 </cn> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 403200 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <apply> <ci> Zeta </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 360 </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'> 7 </cn> </apply> <apply> <times /> <cn type='integer'> 70 </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> <apply> <times /> <cn type='integer'> 280 </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> <apply> <times /> <cn type='integer'> 504 </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'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 720 </cn> <apply> <ci> Zeta </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 172800 </cn> <apply> <ci> Zeta 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</apply> </apply> <apply> <times /> <cn type='integer'> 120960 </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> <ci> Zeta </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6048 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 5 </cn> </apply> <apply> <ci> Zeta </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 22400 </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'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 33600 </cn> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8400 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 33600 </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'> 3 </cn> </apply> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 25200 </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'> 4 </cn> </apply> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 10080 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 5 </cn> </apply> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1680 </cn> <apply> <ci> StieltjesGamma </ci> <cn type='integer'> 6 </cn> </apply> <apply> <ci> Zeta </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 240 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <cn type='integer'> 7 </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'> 10 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 95265 </cn> <apply> <power /> <pi /> <cn type='integer'> 10 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 33 <sep /> 128 </cn> <eulergamma /> <apply> <plus /> <apply> <times /> <cn type='integer'> 11813 </cn> <apply> <power /> <pi /> <cn type='integer'> 8 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </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> <ci> StieltjesGamma </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 11000 </cn> <apply> <power /> <pi /> <cn type='integer'> 6 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </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 /> 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Rule Form





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





2007-05-02





© 1998- Wolfram Research, Inc.