A374677 Decimal expansion of (5/96)*Pi^2 - (log(2)^2)/8.

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

Offset

0,1

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

David Bailey, Peter Borwein, and Simon Plouffe, On the Rapid Computation of Various Polylogarithmic Constants, Mathematics of Computation, Vol. 66, No. 218 (April 1997), pp. 903-913.

Formula

Equals A096615 - A253191/8.

Equals Sum_{k >= 1} d(k)/(2^floor((k + 1)/2)*k^2), where d is the periodic sequence {1, 0, -1, -1, -1, 0, 1, 1}. See Bailey et al. (1997), eq. 2.15, p. 907.

Equals Re(Li_2((1 + i)/2)) = Re(Li_2((1 - i)/2)), where i is the imaginary unit (the imaginary part is A367053 and -A367053, respectively) . - Amiram Eldar, Jun 18 2026

Example

0.4539852691502955833142419237860497501646027251778...

Mathematica

First[RealDigits[5*Pi^2/96 - Log[2]^2/8, 10, 100]]

Crossrefs

Cf. A096615, A253191, A367053.

Sequence in context: A170929 A245085 A299420 * A019836 A388544 A353314

Adjacent sequences: A374674 A374675 A374676 * A374678 A374679 A374680

Keyword

nonn,cons,changed

Author

Paolo Xausa, Jul 16 2024

Status

approved