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Closed Forms for the Apostol-Frobenius-Euler Polynomials

Year: 2025

Type: article

Abstract: The Apostol-Frobenius-Euler polynomials are novel extension from the prolific studies on classical polynomials. In recent years, there has been great erudition focused on evaluating special functions. This paper obtained a simple and finite approach to evaluate the Apostol-Frobenius-Euler polynomials through their closed forms. Closed forms are mathematical expressions expressed using a definite number of standard operations. There can be constants, variables, some elementary operations, and functions, but conventionally, limits are excluded. The researchers utilized some properties of the Bell polynomials of the second kind, the Faà di Bruno formula, and the determinantal representation of the quotient rule to obtain the closed forms. The closed forms for the Apostol-Frobenius-Euler number were also presented.

Source: International Journal For Multidisciplinary Research

DOI: 10.36948/ijfmr.2025.v07i02.41773

Authors: Rashin Nuñez, Jenivive Dabon, Stephany Mae Gelido, Winple Menguito, Wilson Castañeda Jr.

Institutions: University of San Carlos, Cebu Technological University

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

OpenAlex ID: W4409617085

FWCI:

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