**Title:** Arithmetic of Sheffer sequences arising from Riemann, Volkenborn and Kim integrals

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

**Article ID:** MTJPAM-D-21-00078; **Volume 4 / Issue 1 / Year 2022**, Pages 149-169

**Document Type:** Research Paper

**Author(s):** Dae San Kim ^{a} , Taekyun Kim ^{b} , Lee-Chae Jang ^{c} , Hye Kyung Kim ^{d}, Jongkyum Kwon ^{e}

^{a}Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea

^{b}Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea

^{c}Graduate School of Education, Konkuk University, Seoul 05029, Republic of Korea

^{d}Department of Mathematics Education, Daegu Catholic University, Gyeongsan 38430, Republic of Korea

^{e}Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Republic of Korea

Received: 21 December 2021, Accepted: 5 February 2022, Published: 19 February 2022.

** Corresponding Author:** Jongkyum Kwon (Email address: mathkjk26@gnu.ac.kr)

**Full Text:** PDF

**Abstract**

Let {*s*_{n}(*x*)} be any sequence of polynomials with rational coefficients which is Sheffer for some Sheffer pair. Then we consider the Riemann integral from 0 to 1, the Volkenborn integral on ℤ_{p} and the Kim integral on ℤ_{p} of *s*_{n}(*x* + *y*) with respect to *y*. They all give rise to some different Sheffer polynomials. The aim of this paper is to derive some properties of those polynomials, especially their convolution identities, and to illustrate our results with some examples.

**Keywords:** Riemann integral, Volkenborn integral, Kim integral, Umbral calculus

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