A245058 Decimal expansion of the real part of Li_2(I), negated.
2, 0, 5, 6, 1, 6, 7, 5, 8, 3, 5, 6, 0, 2, 8, 3, 0, 4, 5, 5, 9, 0, 5, 1, 8, 9, 5, 8, 3, 0, 7, 5, 3, 1, 4, 8, 6, 5, 2, 3, 6, 8, 7, 3, 7, 6, 5, 0, 8, 4, 9, 8, 0, 4, 7, 1, 6, 9, 4, 4, 7, 7, 8, 6, 7, 1, 2, 5, 0, 9, 3, 3, 8, 0, 0, 4, 0, 0, 1, 0, 9, 2, 2, 9, 2, 0, 3, 6, 1, 2, 5, 7, 7, 4, 6, 9, 8, 3, 8, 1, 6, 3, 0, 0, 0
Offset: 0
Examples
0.2056167583560283045590518958307531486523687376508498047169447786712509338004...
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)
Programs
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Magma
SetDefaultRealField(RealField(100)); R:=RealField(); Pi(R)^2/48; // G. C. Greubel, Aug 25 2018
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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]]
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PARI
zeta(2)/8 \\ Charles R Greathouse IV, Aug 27 2014
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Sage
(pi**2/48).n(200) # F. Chapoton, Mar 16 2020
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
Equals Integral_{x>=0} x/(exp(2*x) + 1) dx. - Kritsada Moomuang, May 29 2025
Comments