A STUDY ON $q$-ANALOGUE OF DEGENERATE $\frac{1}{2}$-CHANGHEE NUMBERS AND POLYNOMIALS
Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 332
DOI: 10.56827/SEAJMMS.2022.1802.1
Author :
Waseem A. Khan (Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box: 1664, Al Khobar 31952, SAUDI ARABIA)
Abstract
The aim of the paper is to introduce $q$-analogue of degenerate $\frac{1}{2}$-Changhee numbers $Ch_{n,q,\lambda,\frac{1}{2}}$ with the help of a $p$-adic $q$-integral on $\mathbb Z_p$ and derive explicit expressions and some identities for those numbers. In more detail, we deduce explicit expressions of $Ch_{n,q,\lambda,\frac{1}{2}}$, as a rational function in terms of Euler number and Stirling numbers of the first kind, as a fermionic $p$-adic $q$-integral on $\mathbb Z_p$.
Keywords and Phrases
Degenerate Catalan numbers, $q$-analogue of degenerate $\frac{1}{2}$-Changhee numbers, $p$-adic $q$-integral on $\mathbb Z_p$.
A.M.S. subject classification
11B83, 11B73, 05A19.
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