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A110544 Decimal expansion of -Integral {x=1..2} log gamma(x) dx. 3
0, 8, 1, 0, 6, 1, 4, 6, 6, 7, 9, 5, 3, 2, 7, 2, 5, 8, 2, 1, 9, 6, 7, 0, 2, 6, 3, 5, 9, 4, 3, 8, 2, 3, 6, 0, 1, 3, 8, 6, 0, 2, 5, 2, 6, 3, 6, 2, 2, 1, 6, 5, 8, 7, 1, 8, 2, 8, 4, 8, 4, 5, 9, 5, 1, 7, 2, 3, 4, 3, 0, 4, 0, 7, 2, 7, 3, 9, 6, 0, 2, 3, 0, 5, 2, 5, 6, 7, 0, 1, 3, 6, 4, 0, 4, 5, 8, 0, 2, 3, 7, 7, 9, 9, 4, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..105.

Eric Weisstein's World of Mathematics, Log Gamma Function.

Eric Weisstein's World of Mathematics, Gamma Function.

FORMULA

Equals zeta'(0)+1 = -1/2*log(2*Pi)+1. - Jean-François Alcover, Jun 10 2013

From Amiram Eldar, Jul 05 2020: (Start)

Equals Sum_{k>=2} (1/(k + 1) - 1/(2*k))*(zeta(k)-1).

Equals Integral_{x=0..1} (1/2 - 1/(1 - x) - 1/log(x)) dx/log(x). (End)

EXAMPLE

0.081061466795327258219670263594382360138602526362216587182848459...

MATHEMATICA

RealDigits[ N[ -Integrate[ Log[ Gamma[ x]], {x, 1, 2}], 128], 10, 128]

RealDigits[ 1/2*Log[2*Pi]-1, 10, 105] // First // Prepend[#, 0]& (* Jean-François Alcover, Jun 10 2013 *)

PROG

(PARI) -intnum(x=1, 2, log(gamma(x))) \\ Michel Marcus, Jul 05 2020

CROSSREFS

Cf. A110543.

Sequence in context: A214097 A194732 A217739 * A320084 A153855 A340065

Adjacent sequences:  A110541 A110542 A110543 * A110545 A110546 A110547

KEYWORD

cons,nonn

AUTHOR

Robert G. Wilson v, Jul 25 2005

STATUS

approved

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Last modified July 24 11:41 EDT 2021. Contains 346273 sequences. (Running on oeis4.)