Interpolatory Taylor and Lidstone series

Abstract

We develop Taylor type series expansions for entire functions of order zero using general interpolation sequences that diverge to infinity sufficiently fast. We also derive two-point and multi-point Lidstone type series expansions for entire functions of order zero. The coefficients of these Taylor and Lidstone type series are expressed in terms of values of a certain integral operator. Our results imply as special cases several recent results on [Formula: see text]-Taylor and [Formula: see text]-Lidstone expansions of order zero entire functions, and provide a general technique for deriving such series.