In this equation (and in (5.17.5) below), the ’s have their principal values on the positive real axis and are continued via continuity, as in §4.2(i).
When in ,
For error bounds and an exponentially-improved extension, see Nemes (2014a). Here is the Bernoulli number (§24.2(i)), and is Glaisher’s constant, given by
and is the derivative of the zeta function (Chapter 25).