A255728 - OEIS

A255728

Decimal expansion of the imaginary part (negated) of the limit (2N -> infinity) of Integral_{1..2N} exp(i*Pi*x)*x^(1/x) dx.

%I #12 Jan 17 2020 16:27:25

%S 6,8,4,0,0,0,3,8,9,4,3,7,9,3,2,1,2,9,1,8,2,7,4,4,4,5,9,9,9,2,6,6,1,1,

%T 2,6,7,1,0,9,9,1,4,8,2,6,5,4,9,9,9,4,3,4,3,2,2,6,3,0,3,7,7,1,3,8,1,5,

%U 3,0,5,8,1,2,4,9,7,6,6,3,8,1,5,0,9,5,9,8,3,4,2,1,2,7,2,1,4,7,8,6,7,2,2

%N Decimal expansion of the imaginary part (negated) of the limit (2N -> infinity) of Integral_{1..2N} exp(i*Pi*x)*x^(1/x) dx.

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 60.

%e -0.6840003894379321291827444599926611267109914826549994343...

%t digits = 103; NIntegrate[x^(1/x)*Sin[Pi*x], {x, 1, Infinity}, WorkingPrecision -> 2*digits] - 1/Pi // RealDigits[#, 10, digits]& // First

%Y Cf. A255727 (real part), A157852.

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, Mar 04 2015