A335028 Decimal expansion of Pi*(exp(1/e) - 1)/2.

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

Offset: 0

Author

Amiram Eldar, May 20 2020

Keywords

• nonn
• cons

Comments

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

Examples

			0.69848264271788427226723035849771244456284836693292...
		

Links

• Harold P. Boas, Cauchy’s Residue Sore Thumb, The American Mathematical Monthly, Vol. 125, No. 1 (2018), pp. 16-28, preprint, arXiv:1701.04887v1 [math.HO], 2017.
• 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.

Crossrefs

Cf. A000796 (Pi), A001113 (e), A019609 (Pi*e), A019610(Pi*e/2), A073229 (e^(1/e)), A335027.

Programs

Mathematica

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

PARI

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

Formula

Equals Integral_{x=0..oo} (exp(cos(x)) * sin(sin(x)) * x /(x^2 + 1)) * dx.