Open AccessStudy on Two New Numbers and Polynomials Numbers and Polynomials Arising from the Fermionic p-adic Integral on \(\mathbb{Z}\)p
Author(s) -
Hye Kyung Kim
Publication year - 2022
Publication title -
journal of advances in mathematics and computer science
Language(s) - English
Resource type - Journals
ISSN - 2456-9968
DOI - 10.9734/jamcs/2022/v37i230436
Subject(s) - catalan number , mathematics , orthogonal polynomials , order (exchange) , difference polynomials , wilson polynomials , discrete orthogonal polynomials , macdonald polynomials , classical orthogonal polynomials , combinatorics , polynomial , generating function , hahn polynomials , discrete mathematics , pure mathematics , gegenbauer polynomials , mathematical analysis , finance , economics
p-adic analysis and their applications is used p-adic distributions, p-adic measure, p-adic integrals, p-adic L-function and other generalized functions. In addition, among the many ways to investigate and construct generating functions for special polynomials and numbers, one of the most important techniques is the p-adic Fermionic integral over \(\mathbb{Z}\)p. In this paper, we introduce new numbers and polynomials arising from the Fermionic p-adic integral on \(\mathbb{Z}\)p. First, we introduce new numbers and polynomials as one of generalizations of Changhee numbers and polynomials of order r (r \(\epsilon\) \(\mathbb{N}\)), which are called the generalized Changhee numbers and polynomials. We explore some interesting identities and explicit formulas of these numbers and polynomials. Second, we define new numbers and polynomials as one of generalizations of Catalan numbers and polynomials of order r (r \(\epsilon\) \(\mathbb{N}\)), which are called the generalized Catalan numbers and polynomials. We also study some combinatorial identities and explicit formulas of these numbers and polynomials.