A227514 - OEIS

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,1

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.

LINKS

Table of n, a(n) for n=0..81.

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

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)

EXAMPLE

0.85776388496070679648018...

MAPLE

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