A319462 Decimal expansion of 1/24 - 1/(8*Pi).

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

Offset

-2,2

Comments

Ramanujan's question 387 in the Journal of the Indian Mathematical Society (IV, 120) asked "Show that Sum_{k>=1} k/(exp(2*Pi*k) - 1) = 1/24 - 1/(8*Pi)".

References

G. H. Hardy, P. V. Sheshu Aiyar and B. M. Wilson, Collected Papers of Srinivasa Ramanujan, Cambridge University Press, 1927, p. 326, Q. 427.

Oskar Schlömilch, Ueber einige unendliche Reihen, Sitzungsberichte der mathematisch-naturwissenschaftlichen Klasse der Sächsischen Akademie der Wissenschaften, Leipzig, 29 (1877), 101-105.

Links

Table of n, a(n) for n=-2..83.

B. C. Berndt, Y. S. Choi and S. Y. Kang, The problems submitted by Ramanujan to the Journal of Indian Math. Soc., in: Continued fractions, Contemporary Math., Vol. 236 (1999), pp. 15-56 (see Q387, JIMS IV).

B. C. Berndt, Y. S. Choi and S. Y. Kang, The problems submitted by Ramanujan to the Journal of Indian Math. Soc., in: Continued fractions, Contemporary Math., Vol. 236 (1999), pp. 15-56 (see Q387, JIMS IV).

S. Ramanujan, Question 387, Indian Mathematical Society (IV, 120).

C. C. Yalavigi, Problem H-176, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 8, No. 5 (1970), p. 488; Keepeing the Q's on Cue, Solution to Problem H-176 by Clyde A. Bridger, ibid., Vol. 10, No. 2 (1972), pp. 186-190.

Index entries for transcendental numbers

Example

0.00187793089369283272444572582353807615805175523155255447974983...

Mathematica

RealDigits[1/24 - 1/(8*Pi), 10, 100][[1]] (* Amiram Eldar, Feb 02 2022 *)

Prog

(PARI) 1/24 - 1/(8*Pi)
(PARI) suminf(k=1, k/(exp(2*Pi*k)-1))

Crossrefs

Sequence in context: A219388 A177218 A342374 * A086911 A327854 A263179

Adjacent sequences: A319459 A319460 A319461 * A319463 A319464 A319465

Keyword

nonn,cons

Author

Hugo Pfoertner, Sep 24 2018

Status

approved