A note on infinite series whose terms involve truncated degenerate exponentials

TL;DR

This paper investigates infinite series involving truncated degenerate exponentials and special numbers, providing explicit evaluations or finite sum representations relevant to degenerate calculus and special functions.

Contribution

It introduces methods to evaluate or express infinite series with truncated degenerate exponentials in terms of finite sums, advancing the understanding of degenerate special functions.

Findings

Explicit values for series involving truncated degenerate exponentials

Finite sum representations of these series

Connections to degenerate gamma and special numbers

Abstract

The degenerate exponentials play an important role in recent study on degenerate versions of many special numbers and polynomials, the degenerate gamma function, the degenerate umbral calculus and the degenerate q-umbral calculus. The aim of this note is to consider infinite series whose terms involve truncated degenerate exponentials together with several special numbers and to find either their values or some other expressions of them as finite sums.