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A318741 Decimal expansion of Pi^3/48 + Pi*log(2)^2/4. 0
1, 0, 2, 3, 3, 1, 1, 0, 1, 2, 2, 3, 6, 3, 7, 0, 3, 2, 3, 0, 8, 4, 8, 2, 0, 5, 0, 4, 0, 8, 8, 4, 8, 6, 7, 3, 8, 3, 1, 8, 7, 2, 0, 9, 7, 6, 7, 4, 7, 3, 2, 8, 1, 3, 0, 3, 0, 5, 1, 3, 4, 2, 7, 6, 3, 6, 2, 9, 5, 3, 3, 4, 3, 9, 7, 5, 6, 0, 8, 6, 6, 8, 2, 9, 2, 3, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The first part of Ramanujan's question 308 in the Journal of the Indian Mathematical Society (III, 168) asked "Show that Integral_{t=0..Pi/2} t * cotan(t) * log(sin(t)) dt  = -Pi^3/48 - Pi*log(2)^2/4".

LINKS

Table of n, a(n) for n=1..87.

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 Q308, JIMS III).

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 Q308, JIMS III).

EXAMPLE

1.0233110122363703230848205040884867383187209767473281303051342763...

PROG

(PARI) Pi^3/48+Pi*log(2)^2/4

(PARI) -intnum(x=0, Pi/2, x*cotan(x)*log(sin(x)))

CROSSREFS

Sequence in context: A021433 A228624 A124798 * A171872 A005135 A290003

Adjacent sequences:  A318738 A318739 A318740 * A318742 A318743 A318744

KEYWORD

nonn,cons

AUTHOR

Hugo Pfoertner, Sep 17 2018

STATUS

approved

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Last modified May 21 19:31 EDT 2019. Contains 323444 sequences. (Running on oeis4.)