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Research Article | Open Access

A q-Type k-Lidstone series for entire functions

Zeinab S. I. Mansour1, Maryam Al-Towailb2( )
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
Department of Computer Science and Engineering, College of Applied Studies and Community Service, King Saud University, Riyadh, KSA
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Abstract

In this paper, we consider the q-type k-Lidstone series. The series follows from expanding certain classes of entire functions in terms of Jackson q − 1 - derivatives at integers congruent to r modulo k, where k is a positive integer. We study the main properties of the fundamental polynomials that appear in the series expansion. We include a detailed study for the case k = 3 with some examples.

Keywords

q-calculusLidstone seriesconvergence seriesq-type Lidstone polynomialsq-difference operator
CLC number: 05A30, 40A05, 41A58, 41A60

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AIMS Mathematics
Volume 8 Issue 6,
June 2023
Pages 13525-13542
DOI: 10.3934/math.2023686

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Cite this article:
Mansour ZSI, Al-Towailb M. A q-Type k-Lidstone series for entire functions. AIMS Mathematics, 2023, 8(6): 13525-13542. https://doi.org/10.3934/math.2023686

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Received: 15 November 2022
Revised: 22 March 2023
Accepted: 27 March 2023
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)