Special Sums

[bmmmburns (Marvin Ray Burns A.G.S. (cum laude))]

Here are two equations many people don’t know.

Attached are the two equations in Mathematica.

[[1]] S.R.Finch, Mathematical Constants, Cambridge, 2003, p. 450

[ [2]] R.J.Mathar, Numerical evaluation of the oscillatory integral
over exp (ipix) x^(1/x) between 1 and infinity arxiv :
0912.3844[math.CA]] [0912.3844] Numerical Evaluation Of the Oscillatory Integral over exp(i*pi*x)*x^(1/x) between 1 and infinity