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A319462 Decimal expansion of 1/24 - 1/(8*Pi). 0
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 (list; constant; graph; refs; listen; history; text; internal format)
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

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

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

EXAMPLE

0.00187793089369283272444572582353807615805175523155255447974983...

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

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Last modified October 21 18:51 EDT 2021. Contains 348155 sequences. (Running on oeis4.)