A255188 Decimal expansion of gamma_1(1/8), the first generalized Stieltjes constant at 1/8 (negated).
1, 6, 6, 4, 1, 7, 1, 9, 7, 6, 3, 6, 0, 9, 3, 1, 5, 6, 6, 2, 8, 4, 1, 9, 2, 6, 2, 3, 0, 3, 7, 3, 9, 4, 4, 9, 2, 8, 5, 1, 3, 2, 6, 6, 0, 6, 5, 4, 7, 4, 4, 5, 5, 2, 9, 4, 2, 9, 3, 7, 9, 2, 5, 1, 8, 2, 2, 9, 3, 6, 5, 2, 4, 9, 2, 2, 3, 8, 1, 5, 7, 1, 5, 4, 1, 4, 5, 7, 7, 1, 7, 3, 9, 1, 9, 0, 6, 3, 2, 0, 7, 5, 6, 8
Offset: 2
Examples
-16.641719763609315662841926230373944928513266065474455...
Links
- G. C. Greubel, Table of n, a(n) for n = 2..5002
- Iaroslav V. Blagouchine, A theorem for the closed-form evaluation of the first generalized Stieltjes constant at rational arguments, arXiv:1401.3724 [math.NT], 2015.
- Iaroslav V. Blagouchine, A theorem ... (same title), Journal of Number Theory Volume 148, March 2015, Pages 537-592.
- Iaroslav V. Blagouchine, Rediscovery of Malmsten’s integrals, their evaluation by contour integration methods and some related results, The Ramanujan Journal October 2014, Volume 35, Issue 1, pp 21-110.
- Iaroslav V. Blagouchine, Rediscovery of Malmsten’s integrals: Full PDF text.
- Eric Weisstein's World of Mathematics, Hurwitz Zeta Function.
- Eric Weisstein's World of Mathematics, Stieltjes Constants.
- Wikipedia, Stieltjes constants
Crossrefs
Programs
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Mathematica
gamma1[1/8] = StieltjesGamma[1] + Sqrt[2]*(Derivative[2, 0][Zeta][0, 1/8] + Derivative[2, 0][Zeta][0, 7/8]) + 2*Pi*Sqrt[2]*LogGamma[1/8] - Pi*Sqrt[2]*(1 - Sqrt[2]) *LogGamma[1/4] - ((1 + Sqrt[2])*(Pi/2) + 4*Log[2] + Sqrt[2]*Log[1 + Sqrt[2]])* EulerGamma - (1/Sqrt[2])*(Pi + 8*Log[2] + 2*Log[Pi])*Log[1 + Sqrt[2]] - 7*((4 - Sqrt[2] )/4)*Log[2]^2 + (1/Sqrt[2])*Log[2]*Log[Pi] - Pi*((10 + 11*Sqrt[2])/4)*Log[2] - Pi*((3 + 2*Sqrt[2])/2)*Log[Pi] // Re; RealDigits[gamma1[1/8], 10, 104] // First (* or, from version 7 up: *) RealDigits[StieltjesGamma[1, 1/8], 10, 104] // First