A continuous analogue of lattice path enumeration: Part II

International audienceFollowing the work of Cano and Díaz, we study continuous binomial coefficients andCatalan numbers. We explore their analytic properties, including integral identities and generaliza-tions of discrete convolutions. We also conduct an in-depth analysis of a continuous analogue of thebinomial distribution, including a stochastic representation as a Goldstein-Kac process