A121225 - OEIS

A121225

Decimal expansion of -log(2-2*cos(1))/2.

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

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OFFSET

-1,1

COMMENTS

From Bernard Schott, Apr 20 2021: (Start)

The series Sum_{k>=1} cos(k)/k and also Sum_{k>=1} sin(k)/k (A096444) are called Fresnel series.

Abel summation shows these two series are convergent.

The series Sum_{k>=1} |cos(k)/k| is divergent. (End)

REFERENCES

Xavier Merlin, Methodix Analyse, Ellipses, 1997, p. 117.

LINKS

Table of n, a(n) for n=-1..98.