Conditional Expanding of Functions by <i>q</i>-Lidstone Series

Abstract

This paper characterizes those functions given by convergent q-Lidstone series expansion. We give the necessary and sufficient conditions so that the entire function f(z) has such an expansion, in which case convergence is uniform on compact sets.

Keywords

• <i>q</i>-Lidstone series
• <i>q</i>-Lidstone polynomials
• asymptotic expansion
• convergence series