A class of laplace transforms arising in a diffusion problem

It is shown that the function [α + (1 + 2s)^1/2]^?1, s ≥ 0, with fixed α ≥ ?1, is the Laplace transform of an explicitly given non-negative function g(x;α), × ≥ 0. This class of functions has easily computable convolutions. This property is used to identify the distribution of a sojourn time integral for the diffusion defined as Brownian motion on the real line with constant drift to the origin. © 1994 John Wiley & Sons, Inc.