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A256273
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Decimal expansion of Integral_{0..infinity} exp(-x^2)*cosh(sqrt(1+x^2)) dx.
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2
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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
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OFFSET
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1,2
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LINKS
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FORMULA
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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.
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EXAMPLE
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1.661095845547755702622913937539905964012699504156022...
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MAPLE
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evalf(Int(exp(-x^2)*cosh(sqrt(1+x^2)), x=0..infinity), 120); # Vaclav Kotesovec, Jun 02 2015
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MATHEMATICA
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NIntegrate[Exp[-x^2]*Cosh[Sqrt[1 + x^2]], {x, 0, Infinity}, WorkingPrecision -> 105] // RealDigits // First
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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