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

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, 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, 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

Offset: 1

Author

Jean-François Alcover, Jun 02 2015

Keywords

• nonn
• cons
• easy

Examples

			1.661095845547755702622913937539905964012699504156022...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000
• MathOverflow, Improper integral Integral_{0..infinity} exp(-a*x^2)*cosh(b*sqrt(1+x^2))
• Eric Weisstein's MathWorld, Beta Function

Programs

Maple

evalf(Int(exp(-x^2)*cosh(sqrt(1+x^2)), x=0..infinity), 120); # Vaclav Kotesovec, Jun 02 2015

Mathematica

NIntegrate[Exp[-x^2]*Cosh[Sqrt[1 + x^2]], {x, 0, Infinity}, WorkingPrecision -> 105] // RealDigits // First

Formula

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.