Expressions: a series sum(k, lo, hi, body) (integer bounds, up to 1000000 terms, nested up to four deep), Bessel functions of integer order besselj(n, x) and bessely(n, x), and the Kelvin functions ber(x) and bei(x), in velocity sources and particle values. picurv validates the special functions but leaves their evaluation to the solver, so ic_gen expressions cannot use them. The initial-conditions page gives exact rectangular-duct Poiseuille and Womersley pipe-flow sources written with them.