In this paper we use the Siegert formula to derive alternative expressions for the moments of the first passage time of the Ornstein-Uhlenbeck process through a constant threshold. The expression for the nth moment is recursively linked to the lower-order moments and consists of only n terms. These compact expressions can substantially facilitate (numerical) applications also for higher-order moments.
"A recursion formula for the moments of the first passage time of the Ornstein-Uhlenbeck process." J. Appl. Probab. 52 (2) 595 - 601, June 2015. https://doi.org/10.1239/jap/1437658618