λ-q-Sheffer sequence and its applications

Abstract

Recently, Kim-Kim [J. Math. Anal. Appl. 493 (2021), no. 1] introduced the degenerate Sheffer sequence and λ-Sheffer sequence. The purpose of this article is to study λ-q-Sheffer sequence and the degenerate q-Sheffer sequence, which are derived from the view point of degenerate umbral calculus and investigate some properties related to those sequences. In addition, we give some new identities associated with q-special polynomials arising from our investigation.

Keywords

• q-exponential functions
• q-umbral calculus
• λ-umbral calculus
• q-bernoulli polynomials
• q-euler polynomials
• 05a30
• 05a40
• 11b68