OFFSET
0,1
COMMENTS
This constant links Euler's constant and Pi to the values of the Riemann zeta function at positive integers (see formulas).
REFERENCES
D. Suryanarayana, Sums of Riemann zeta function, Math. Student, 42 (1974), 141-143.
LINKS
Stefano Spezia, Table of n, a(n) for n = 0..10000
B. Candelpergher, Ramanujan summation of divergent series, HAL Id : hal-01150208; Lecture Notes in Math. Series (Springer), 2185, (2017), 93.
Marc-Antoine Coppo, On certain alternating series involving zeta and multiple zeta values. 2018. <hal-01735381v4>.
R. J. Singh, V. P. Verma, Some series involving Riemann zeta function, Yokohama Math. J. 31 (1983), 1-4.
H. M. Srivastava, Sums of certain series of the Riemann zeta function, J. Math. Anal. App. 134 (1988), 129-140.
FORMULA
EXAMPLE
0.369669299246093688522926308635583575659682194332178386585...
MAPLE
Digits := 100; evalf((1/2)*(gamma-ln(2*Pi))+1);
MATHEMATICA
First[RealDigits[N[(1/2)*(EulerGamma-Log[2*Pi])+1, 100], 10]]
PROG
(PARI) (1/2)*(Euler-log(2*Pi))+1
(Python)
from mpmath import *
mp.dps = 100; mp.pretty = True
+(1/2)*(euler-log(2*pi))+1
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Stefano Spezia, Dec 12 2018
STATUS
approved