A227514 Decimal expansion of the square root of 2/e.

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

Offset: 0

Author

R. J. Mathar, Jul 14 2013

Keywords

• cons
• nonn
• easy

Comments

This appears for example while integrating the product of the absolute value of H_2(x) exp(-x^2) over the real line, where H_2 is the second Hermite polynomial.

Examples

			0.85776388496070679648018...
		

Links

• R. J. Mathar, Orthogonal linear combinations of Gaussian Type Orbitals, arXiv:physics/9907051 [physics.chem-ph], 1999-2009, Section VII.

Crossrefs

Cf. A001113, A002193, A019774, A135002.

Programs

Maple

evalf(sqrt(2/exp(1))) ;

Mathematica

RealDigits[Sqrt[2/E], 10, 120][[1]] (* Amiram Eldar, Jul 08 2023 *)

PARI

sqrt(2/exp(1)) \\ Charles R Greathouse IV, Apr 16 2014

Formula

Square root of A135002 and also the ratio A002193 / A019774 .

From Amiram Eldar, Jul 08 2023: (Start)

Equals Product_{n>=1} (e / (1 + 1/(n-1/2))^n).

Equals Product_{n>=1} (e * (1 - 1/(n+1/2))^n). (End)