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

2,2

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

Example

-16.641719763609315662841926230373944928513266065474455...

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

Crossrefs

Cf. A001620 (gamma), A082633 (gamma_1), A254327 (gamma_1(1/2)), A254331 (gamma_1(1/3)), A254345 (gamma_1(2/3)), A254347 (gamma_1(1/4)), A254348 (gamma_1(3/4)), A254349 (gamma_1(1/6)), A254350 (gamma_1(5/6)), A251866 (gamma_1(1/5)).

Sequence in context: A214581 A094888 A159702 * A164510 A019957 A099405

Adjacent sequences: A255185 A255186 A255187 * A255189 A255190 A255191

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Feb 16 2015

Status

approved