# §5.17 Barnes’ -Function (Double Gamma Function)

5.17.1

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 ,

see Ferreira and López (2001). This reference also provides bounds for the error term. Here is the Bernoulli number (§24.2(i)), and is Glaisher’s constant, given by

5.17.6

where

5.17.7

and is the derivative of the zeta function (Chapter 25).

For Glaisher’s constant see also Greene and Knuth (1982, p. 100) and §2.10(i).