A $ q $-Type $ k $-Lidstone series for entire functions

Abstract

In this paper, we consider the $ q $-type $ k $-Lidstone series. The series follows from expanding certain classes of entire functions in terms of Jackson $ q^{-1} $- derivatives at integers congruent to r modulo k, where $ k $ is a positive integer. We study the main properties of the fundamental polynomials that appear in the series expansion. We include a detailed study for the case $ k = 3 $ with some examples.

Keywords

• $ q $-calculus
• lidstone series
• convergence series
• $ q $-type lidstone polynomials
• $ q $-difference operator