Degenerate Fubini-type polynomials associated with degenerate Apostol-Bernoulli and Apostol-Euler polynomials of order {\alpha}

TL;DR

This paper introduces degenerate Fubini-type polynomials, explores their relations with degenerate Apostol-Bernoulli and Euler polynomials, and derives new formulas and recurrence relations using generating functions and Bell polynomials.

Contribution

It presents the first introduction of degenerate Fubini-type polynomials and establishes their connections with other degenerate special polynomials, along with new explicit formulas and recurrence relations.

Findings

Derived new explicit formulas for Fubini-type polynomials.

Established relations between degenerate Fubini-type and Apostol-Bernoulli/Euler polynomials.

Presented recurrence relations for these polynomials.

Abstract

In this paper, by introducing the degenerate Fubini-type polynomials, we give several relations with the help of the Fa\`a di Bruno formula and some properties of Bell polynomials, and generating function methods. Also, we derive some new explicit formulas and recurrence relations for Fubini-type polynomials and numbers. Associating the degenerate Fubini-type polynomials newly defined here with degenerate Apostol-Bernoulli polynomials and degenerate Apostol-Euler polynomials of order {\alpha} enables us to present additional relations for some degenerate special polynomials and numbers.