A114940 -id:A114940 - cp's OEIS frontend

A114941 Decimal expansion of the infinite sum Sum_{k>=1} cos(k)/k!.

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

Offset: 0

Stefan Steinerberger, Feb 21 2006

			0.143835643791640325906...

Cf. A001113, A049469, A049470, A114940.

RealDigits[Sum[N[Cos[i],400]/i!, {i,1,300}]][[1]] (*which is accurate to 300 digits*) (* corrected by Harvey P. Dale, Nov 29 2011 *)

suminf(k=1, cos(k)/k!) \\ Michel Marcus, Jul 19 2020

From Amiram Eldar, Jul 19 2020: (Start)
Equals e^cos(1) * cos(sin(1)) - 1.
Equals cos(sin(1)) * (cosh(cos(1)) + sinh(cos(1))) - 1.
Equals (e^(e^i) + e^(e^(-i)))/2 - 1. (End)

A351738 Decimal expansion of Sum_{k>0} sin(sqrt(k)) / k.

Original entry on oeis.org

1, 7, 1, 5, 6, 7, 1, 7, 9, 4, 7, 0, 9

Offset: 1

Bernard Schott, May 20 2022

Sum_{k>0} sin(k^alpha) / (k^beta) with 0 < alpha < 1 is convergent if beta > max(alpha, 1-alpha); the constant of this sequence corresponds to the case alpha = 1/2 and beta = 1 (see Arnaudiès).
Consequence: Sum_{k>0} sin(k^(1/m)) / k converges for any positive integer m.
The sequence converges slowly.

			1.715671794709...

J. M. Arnaudiès, P. Delezoide et H. Fraysse, Exercices résolus d'Analyse du cours de mathématiques - 2, Dunod, 1993, Exercice 11, pp. 316-319.

Mathematics Stack Exchange, Convergence of Sum_{k=0..infinity} sin(sqrt(k)) / k.

Cf. A096418, A096444, A114940, A228639, A263193, A342680.

default(realprecision, 100); sumalt(k=0, sum(j=1+floor(k^2*Pi^2),floor((k+1)^2*Pi^2), sin(sqrt(j))/j)) \\ Vaclav Kotesovec, May 21 2022

More digits from Stefano Spezia, May 21 2022

cp's OEIS Frontend

A114941 Decimal expansion of the infinite sum Sum_{k>=1} cos(k)/k!.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

PARI

Formula

A351738 Decimal expansion of Sum_{k>0} sin(sqrt(k)) / k.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

PARI

Extensions