OFFSET
0,1
COMMENTS
This is the decimal expansion of the real part of the dilogarithm of the square root of -1. The imaginary part is Catalan's number (A006752).
5*Pi^2/24 = 10 * (this constant) equals the asymptotic mean of the abundancy index of the even numbers. - Amiram Eldar, May 12 2023
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000 (terms 0..104 from Robert G. Wilson v)
R. J. Mathar, Some definite integrals over a power multiplied by four modified Bessel functions vixra:1606.0141 (2016) eq. (39)
Paul J. Nahin, Inside interesting integrals, Undergrad. Lecture Notes in Physics, Springer (2020), (6.3.13)
FORMULA
Also equals -zeta(2)/8 = -Pi^2/48.
Also equals the Bessel moment Integral_{0..inf} x I_1(x) K_0(x)^2 K_1(x) dx. - Jean-François Alcover, Jun 05 2016
From Terry D. Grant, Sep 11 2016: (Start)
Equals Sum_{n>=0} (-1)^n/(2n+2)^2.
Equals (Sum_{n>=1} 1/(2n)^2)/2 = A222171/2. (End)
Equals Sum_{k>=1} A007949(k)/k^2. - Amiram Eldar, Jul 13 2020
Equals a tenth of integral_0^{pi/2} arccos[cos x/(1+2 cos x)]dx [Nahin]. - R. J. Mathar, May 22 2024
EXAMPLE
0.2056167583560283045590518958307531486523687376508498047169447786712509338004...
MATHEMATICA
RealDigits[ Re[ PolyLog[2, I]], 10, 111][[1]] (* or *) RealDigits[ Zeta[2]/8, 10, 111][[1]] (* or *) RealDigits[ Pi^2/48, 10, 111][[1]]
PROG
(PARI) zeta(2)/8 \\ Charles R Greathouse IV, Aug 27 2014
(Sage)
(pi**2/48).n(200) # F. Chapoton, Mar 16 2020
(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); Pi(R)^2/48; // G. C. Greubel, Aug 25 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Robert G. Wilson v, Aug 21 2014
STATUS
approved