New type degenerate Simsek numbers and related aspects

TL;DR

This paper introduces a new class of degenerate Simsek numbers, providing their generating functions, explicit formulas, recurrence relations, and exploring their connections with other special numbers, supported by numerical and graphical analysis.

Contribution

The paper presents a novel type of degenerate Simsek numbers, along with their generating functions, formulas, and relations, expanding the understanding of these special sequences.

Findings

Derived explicit formulas and recurrence relations for the new numbers.

Established connections between the new numbers and existing special numbers.

Provided numerical examples and graphical illustrations of the new numbers.

Abstract

In this paper, we introduce a new type degenerate Simsek numbers and their generating function, which are different from degenerate Simsek number studied so far. We establish the explicit formula, recurrence relation and other identities for these numbers. We also derive several interesting expressions and relations between these numbers and certain other special numbers in the literature. In addition, several numerical examples and graphical illustrations are provided to support the theoretical results and to illustrate the behavior of the introduced numbers.