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A255188 Decimal expansion of gamma_1(1/8), the first generalized Stieltjes constant at 1/8 (negated). 10
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
2,2
LINKS
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.
Eric Weisstein's World of Mathematics, Hurwitz Zeta Function.
Eric Weisstein's World of Mathematics, 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
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved

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Last modified July 20 15:09 EDT 2024. Contains 374459 sequences. (Running on oeis4.)