A new integral representation for the Barnes double gamma function is derived. This is canonical in the sense that solutions to a class of functional difference equations of first order with trigonometrical coefficients can be expressed in terms of the Barnes function. The integral representation given here makes these solutions very simple to compute. Several well-known difference equations are solved by this method and a treatment of the linear theory for moving contact line flow in an inviscid fluid wedge is given.https://journals.cambridge.org/action/displayAbstract?aid=231870
