A selected survey of umbral calculus (Q1909967)

Summary: We survey the mathematical literature on umbral calculus (otherwise known as the calculus of finite difference) from its roots in the 19th century (and earlier) as a set of ``magic rules'' for lowering and raising indices, through its rebirth in the 1970's as Rota's school set it on a firm logical foundation using operator methods, to the current state of the art with numerous generalizations and applications. The survey itself is complemented by a fairly complete bibliography (over 400 references) which we expect to update regularly.