A256848 Decimal expansion of the generalized Euler constant gamma(3,5) (negated).

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

Offset

0,3

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(5)/5 - PolyGamma(3/5)/5.

Equals EulerGamma/5 + Pi/(10*sqrt(2*(5+sqrt(5)))) - Pi/(2*sqrt(10*(5+sqrt(5)))) + log(5)/20 + log((5-sqrt(5))/(5+sqrt(5)))/(4*sqrt(5)).

Example

-0.013763739708181991968019076883991139603013419915782102729...

Mathematica

Join[{0}, RealDigits[-Log[5]/5 - PolyGamma[3/5]/5, 10, 108] // First  ]

Prog

(PARI) default(realprecision, 100); Euler/5 + Pi/(10*sqrt(2*(5+sqrt(5)))) - Pi/(2*sqrt(10*(5+sqrt(5)))) + log(5)/20 + log((5-sqrt(5))/(5+sqrt(5)))/(4*sqrt(5)) \\ G. C. Greubel, Aug 28 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)/5 + Pi(R)/(10*Sqrt(2*(5+Sqrt(5)))) - Pi(R)/(2*Sqrt(10*(5+Sqrt(5)))) + Log(5)/20 + Log((5-Sqrt(5))/(5+Sqrt(5)))/(4*Sqrt(5)); // 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: A388906 A301814 A065281 * A019952 A157699 A283270

Adjacent sequences: A256845 A256846 A256847 * A256849 A256850 A256851

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 11 2015

Status

approved