A335028 -id:A335028 - cp's OEIS frontend

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

Amiram Eldar, May 20 2020

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.

			2.69907078454188691350045374313353580541885956819500...

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.

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

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

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

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.

cp's OEIS Frontend

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

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