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%I #12 Jul 08 2023 04:12:10
%S 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,
%T 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,
%U 9,9,8,4,0,1,8,3,0,0,2,1,6,0
%N Decimal expansion of the square root of 2/e.
%C 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.
%H R. J. Mathar, <a href="http://arxiv.org/abs/physics/9907051">Orthogonal linear combinations of Gaussian Type Orbitals</a>, arXiv:physics/9907051 [physics.chem-ph], 1999-2009, Section VII.
%F Square root of A135002 and also the ratio A002193 / A019774 .
%F From _Amiram Eldar_, Jul 08 2023: (Start)
%F Equals Product_{n>=1} (e / (1 + 1/(n-1/2))^n).
%F Equals Product_{n>=1} (e * (1 - 1/(n+1/2))^n). (End)
%e 0.85776388496070679648018...
%p evalf(sqrt(2/exp(1))) ;
%t RealDigits[Sqrt[2/E], 10, 120][[1]] (* _Amiram Eldar_, Jul 08 2023 *)
%o (PARI) sqrt(2/exp(1)) \\ _Charles R Greathouse IV_, Apr 16 2014
%Y Cf. A001113, A002193, A019774, A135002.
%K cons,nonn,easy
%O 0,1
%A _R. J. Mathar_, Jul 14 2013
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