A335027 Decimal expansion of Pi*(e-1)/2.

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

Offset

1,1

Comments

The value of an integral (see formula) first calculated by Cauchy in 1825 (with an error that was corrected in 1826).

This integral appears in the forward to Vălean's book, written by Paul J. Nahin.

Links

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

Augustin-Louis Cauchy, Mémoire sur les intégrales définies prises entre des limites imaginaires, Paris, 1825, p. 65, equation 24.

Augustin-Louis Cauchy, Exercices de mathématiques, Paris, 1826, p. 108, equation 48.

Edward Thomas Copson, An Introduction to the Theory of Functions of a Complex Variable, London, 1935, Oxford, 1972 edition, p. 153.

Paul J. Nahin, Inside Interesting Integrals, Springer-Verlag New York, 2015, p. 340.

Cornel Ioan Vălean, (Almost) Impossible Integrals, Sums, and Series, Springer International Publishing, 2019, p. 206-207.

Formula

Equals Integral_{x=0..oo} (exp(cos(x)) * sin(sin(x))/x) * dx (Cauchy, 1825-26).

Equals Integral_{x=0..oo} (exp(cos(x)) * sin(x) * sin(sin(x))/x^2) * dx (Vălean, 2019).

Equals A019610 - A019669.

Example

2.69907078454188691350045374313353580541885956819500...

Mathematica

RealDigits[Pi*(E-1)/2, 10, 100][[1]]

Prog

(PARI) Pi*(exp(1)-1)/2 \\ Michel Marcus, May 20 2020

Crossrefs

Cf. A000796 (Pi), A001113 (e), A019609 (Pi*e), A019610(Pi*e/2), A019669 (Pi/2), A335028.

Sequence in context: A136701 A374695 A175030 * A263178 A198230 A263495

Adjacent sequences: A335024 A335025 A335026 * A335028 A335029 A335030

Keyword

nonn,cons

Author

Amiram Eldar, May 20 2020

Status

approved