

A342647


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


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OFFSET

0,1


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.


REFERENCES

JeanMarie Monier, Analyse, Exercices corrigés, 2ème année MP, Dunod, 1997, Exercice 3.2.1.f p. 279.


LINKS



FORMULA

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


EXAMPLE

0.588251433968163564741783117942531437228475727762559...


PROG

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


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STATUS

approved



