cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A342647 Decimal expansion of Sum_{n>=1} log(cos(1/n)) * log(sin(1/n)).

Original entry on oeis.org

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Offset: 0

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Author

Bernard Schott, Mar 17 2021

Keywords

Comments

log(cos(1/n)) ~ -1/(2*n^2) when n -> oo, so the series log(cos(1/n)) is convergent (A336603), but
log(sin(1/n)) ~ -log(n) when n -> oo, so the series log(sin(1/n)) is divergent.
However, as log(cos(1/n)) * log(sin(1/n)) ~ log(n)/(2*n^2) when n -> oo, the series log(cos(1/n)) * log(sin(1/n)) is convergent.

Examples

			0.588251433968163564741783117942531437228475727762559...

References

  • Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année MP, Dunod, 1997, Exercice 3.2.1.f p. 279.

Crossrefs

Cf. A336405, A336603.

Programs

  • PARI
    sumpos(n=1, log(cos(1/n)) * log(sin(1/n))) \\ Michel Marcus, Mar 18 2021

Formula

Equals Sum_{n>=1} log(cos(1/n)) * log(sin(1/n)).

Extensions

a(4)-a(51) from Jon E. Schoenfield, Mar 18 2021
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