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A335027 Decimal expansion of Pi*(e-1)/2. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
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
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: A246828 A136701 A175030 * A263178 A198230 A263495
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, May 20 2020
STATUS
approved

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Last modified May 21 05:34 EDT 2024. Contains 372728 sequences. (Running on oeis4.)