Article ID: MTJPAM-D-23-00058

Title: A note on parametric Apostol-Bernoulli type polynomials

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-23-00058; Volume 7 / Issue 1 / Year 2025, Pages 157-166

Document Type: Research Paper

Author(s): ‪Seçil İçiuyan ^a‪

^aDepartment of Computer Programming, Anadolu Bil Vocational School, Istanbul Aydin University, Turkey

Received: 14 December 2023, Accepted: 12 May 2025, Published: 25 October 2025

Corresponding Author: ‪Seçil İçiuyan (Email address: secilbilgic@aydin.edu.tr)

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Abstract

In this paper, we examine two parametric kinds of Apostol-Bernoulli, Apostol-Euler, and Apostol-Gennochi polynomials, which are generalizations of the classical Bernoulli, Euler, and Genocchi polynomials, and the second type, unified Apostol-Bernoulli type polynomials. Later, inspired by these studies, we give some polynomial expressions. We obtain some general forms of the polynomials expressed by many authors. Then, we give some theorems and results about these polynomials. Finally, we prove that the symmetric relation holds.

Keywords: Second type parametric unified Apostol-Bernoulli type polynomials, second type unified Apostol-Bernoulli type polynomials, second type parametric generalized Apostol-Bernoulli polynomials, second type parametric generalized Apostol-Euler polynomials, the second type parametric generalized Apostol-Genocchi polynomials, generalized Stirling numbers of the second kind

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