A159275 Decimal expansion of integral(t=0,1,zeta(t)+1/(1-t))=0.539298676...

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

Offset

0,1

Comments

The function zeta(t)+1/(1-t)) being almost linear between 0 and 1, the integral is near 1/4 + EulerGamma/2 = 0.5386... - Jean-François Alcover, Nov 08 2012

Links

Table of n, a(n) for n=0..99.

Maple

Digits := 100 ; H := proc(n) option remember ; if n < 1 then 0 ; elif n = 1 then 1; else procname(n-1)+1/n ; fi; end: bn := proc(n) n*(1-gamma-H(n-1))-1/2+add(binomial(n, k)*(-1)^k*Zeta(k), k=2..n) ; end: x := 0.0 ; for n from 0 do ints := expand(binomial(s, n)) ; ints := int(ints, s=0..1) ; x := x+evalf((-1)^n*bn(n)*ints) ; printf("%.40f\n", 1+x) ; od: # J Comp Appl Math 220 (2008) 58. - R. J. Mathar, May 19 2009

Mathematica

RealDigits[ N[ Integrate[Zeta[t] + 1/(1-t), {t, 0, 1}] , 105]][[1]] (* Jean-François Alcover, Nov 08 2012 *)

Prog

(PARI) intnum(t=0, 1, zeta(t)+1/(1-t)) \\ Charles R Greathouse IV, Mar 10 2016

Crossrefs

Sequence in context: A305327 A112812 A241624 * A374990 A059031 A245516

Adjacent sequences: A159272 A159273 A159274 * A159276 A159277 A159278

Keyword

cons,nonn

Author

Benoit Cloitre, Apr 07 2009

Extensions

Leading zero removed by R. J. Mathar, May 19 2009

Status

approved