A350762 Decimal expansion of Sum_{k>=1} ((-1)^(k+1) * (log(2) - Sum_{j=1..k} 1/(k+j))^2).

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

Offset

-1,1

References

Ovidiu Furdui, Limits, Series, and Fractional Part Integrals, Springer, 2013, section 3.71, pp. 196-199.

Links

Table of n, a(n) for n=-1..103.

Ovidiu Furdui and Huizeng Qin, Problem H-691, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 48, No. 3 (2010), p. 283; Catalan's Constant, Pi and ln(2), Solution to Problem H-691 by Khristo N. Boyadzhiev, ibid., Vol. 50, No. 1 (2012), pp. 90-92; Errata, ibid., Vol. 50, No. 4 (2012), p. 381.

Khristo N. Boyadzhiev, On a series of Furdui and Qin and some related integrals, arXiv:1203.4618 [math.NT], 2012.

Formula

Equals 7*log(2)^2/8 + Pi*log(2)/8 - G/2 - Pi^2/48, where G is Catalan's constant (A006752).

Example

0.02899509302173870080994716951858838964211337039970...

Mathematica

RealDigits[7*Log[2]^2/8 + Pi*Log[2]/8 - Catalan/2 - Pi^2/48, 10, 100][[1]]

Crossrefs

Cf. A000796, A002162, A006752, A102886.

Sequence in context: A145426 A200499 A298525 * A081101 A043059 A237415

Adjacent sequences: A350759 A350760 A350761 * A350763 A350764 A350765

Keyword

nonn,cons

Author

Amiram Eldar, Jan 14 2022

Status

approved