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A256273 Decimal expansion of Integral_{0..infinity} exp(-x^2)*cosh(sqrt(1+x^2)) dx.

%I A256273 #13 Feb 16 2025 08:33:25
%S A256273 1,6,6,1,0,9,5,8,4,5,5,4,7,7,5,5,7,0,2,6,2,2,9,1,3,9,3,7,5,3,9,9,0,5,
%T A256273 9,6,4,0,1,2,6,9,9,5,0,4,1,5,6,0,2,2,0,0,7,2,8,4,3,5,9,1,4,1,2,9,9,7,
%U A256273 5,8,3,5,2,1,5,4,6,8,1,5,2,8,1,7,6,2,9,7,4,4,0,3,3,0,6,9,7,9,4,3,3,7,1,7,0
%N A256273 Decimal expansion of Integral_{0..infinity} exp(-x^2)*cosh(sqrt(1+x^2)) dx.
%H A256273 G. C. Greubel, <a href="/A256273/b256273.txt">Table of n, a(n) for n = 1..5000</a>
%H A256273 MathOverflow, <a href="http://mathoverflow.net/questions/167697">Improper integral Integral_{0..infinity} exp(-a*x^2)*cosh(b*sqrt(1+x^2))</a>
%H A256273 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/BetaFunction.html">Beta Function</a>
%F A256273 Also equals sqrt(Pi)*Sum_{n>=0} (Sum_{k>=n} (-1)^n*k!/((2*k)!*Beta(n + 1, 1/2 - n)*(k - n)!)), where Beta is the Euler beta function.
%e A256273 1.661095845547755702622913937539905964012699504156022...
%p A256273 evalf(Int(exp(-x^2)*cosh(sqrt(1+x^2)), x=0..infinity), 120); # _Vaclav Kotesovec_, Jun 02 2015
%t A256273 NIntegrate[Exp[-x^2]*Cosh[Sqrt[1 + x^2]], {x, 0, Infinity}, WorkingPrecision -> 105] // RealDigits // First
%K A256273 nonn,cons,easy
%O A256273 1,2
%A A256273 _Jean-François Alcover_, Jun 02 2015