A256846 Decimal expansion of the generalized Euler constant gamma(3,4) (negated).

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

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

D. H. Lehmer, Euler constants for arithmetic progressions, Acta Arith. 27 (1975) p. 134.

Formula

Equals -log(2)/2 - PolyGamma(3/4)/4 = EulerGamma/4 - Pi/8 + log(2)/4. [simplified by Vaclav Kotesovec, Apr 22 2026]

Example

-0.07510837033335461230189437002479311074523130734684351439...

Mathematica

Join[{0}, RealDigits[-Log[2]/2 - PolyGamma[3/4]/4, 10, 104] // First ]

Prog

(PARI) default(realprecision, 100); Euler/4 - Pi/8 - log(4)/4 + log(8)/4 \\ G. C. Greubel, Aug 28 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)/4 - Pi(R)/8 - Log(4)/4 + Log(8)/4; // G. C. Greubel, Aug 28 2018

Crossrefs

Cf. A001620 (gamma(1,1) = EulerGamma),

Primitive ruler-and-compass constructible gamma(r,k): A228725 (1,2), A256425 (1,3), A256778 (1,4), A256779 (1,5), A256780 (2,5), A256781 (1,8), A256782 (3,8), A256783 (1,12), A256784 (5,12),

Other gamma(r,k) (1 <= r <= k <= 5): A239097 (2,2), A256843 (2,3), A256844 (3,3), A256845 (2,4), A256846 (3,4), A256847 (4,4), A256848 (3,5), A256849 (4,5), A256850 (5,5).

Sequence in context: A350544 A386740 A396261 * A336698 A241837 A145176

Adjacent sequences: A256843 A256844 A256845 * A256847 A256848 A256849

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 11 2015

Status

approved