A255189 Decimal expansion of gamma_1(1/12), the first generalized Stieltjes constant at 1/12 (negated).

2, 9, 8, 4, 2, 8, 7, 8, 2, 3, 2, 0, 4, 1, 3, 3, 1, 3, 0, 3, 3, 5, 1, 0, 2, 0, 2, 6, 0, 7, 5, 9, 2, 6, 3, 2, 3, 9, 8, 9, 2, 0, 4, 4, 0, 0, 1, 8, 6, 1, 0, 0, 5, 6, 8, 7, 0, 3, 6, 1, 0, 6, 7, 8, 3, 0, 9, 3, 3, 3, 8, 8, 5, 1, 5, 6, 1, 2, 3, 1, 6, 1, 4, 6, 4, 6, 2, 5, 1, 2, 7, 6, 9, 7, 0, 1, 2, 4, 2, 3, 4, 8, 7, 8

Offset

2,1

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 and some related summations, Journal of Number Theory (Elsevier), Volume 148, pages 537-592, March 2015 (arXiv preprint).

Eric Weisstein's MathWorld, Hurwitz Zeta Function.

Eric Weisstein's MathWorld, Stieltjes Constants.

Wikipedia, Stieltjes constants

Example

-29.842878232041331303351020260759263239892044001861...

Mathematica

gamma1[1/12] = StieltjesGamma[1] + Sqrt[3]*(Derivative[2, 0][Zeta][0, 1/12] + Derivative[2, 0][Zeta][0, 11/12]) + 4*Pi*LogGamma[1/4] + 3*Pi*Sqrt[3]*LogGamma[1/3] - (((2 + Sqrt[3])/2)*Pi + (3/2)*Log[3] - Sqrt[3]*(1 - Sqrt[3])*Log[2] + 2*Sqrt[3]*Log[1 + Sqrt[3]])*EulerGamma - 2*Sqrt[3]*(3*Log[2] + Log[3] + Log[Pi])* Log[1 + Sqrt[3]] - ((7 - 6*Sqrt[3])/2)*Log[2]^2 - (3/4)*Log[3]^2 + 3*Sqrt[3]*((1 - Sqrt[3])/2)*Log[3]*Log[2] + Sqrt[3]*Log[2]*Log[Pi] - Pi*((17 + 8*Sqrt[3])/(2*Sqrt[3]))*Log[2] + ((Pi*(1 - Sqrt[3])*Sqrt[3])/4)*Log[3] - Pi*Sqrt[3]*(2 + Sqrt[3])*Log[Pi] // Re; RealDigits[gamma1[1/12], 10, 104] // First
(* or, from version 7 up: *) RealDigits[StieltjesGamma[1, 1/12], 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)) A255188 (gamma_1(1/8)).

Sequence in context: A329992 A125124 A011446 * A309211 A021339 A092971

Adjacent sequences: A255186 A255187 A255188 * A255190 A255191 A255192

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Feb 16 2015

Status

approved