where it is written as the sum of sin, cos, and sum(-1)^r/r^(1/2)

This constant is the convergence of the sum (-1)^r/r^(1/2)

where r = 1, 2, 3, 4, ... or

1-1/sqrt(2)+1/sqrt(3)+...

for terms

999 .6207139841

1000 .5890912075

9999 .6098987708

10000 .5998987708

14999 .6089811921

15000 .6008162263

49999 .6071347136

50000 .6026625776

Notice that this sum is close to 1/sqrt(e) = 0.6065306597...

Milton L. Brown