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Inverse Relations for Certain Sheffer Sequences

SIAM Journal on Mathematical Analysis, 1981
Let $s_n (x)(n = 0,1,2, \cdots )$ be a so-called Sheffer sequence of polynomials, and let $a_n (n = 0,1,2, \cdots )$ be a sequence of the type $a_n = yn + z$ where y and z are constants. An expansion formula for each polynomial $s_n (x)$ in terms of the sequence $s_n (x + a_n )(n = 0,1,2, \cdots )$ is derived, and the formula is illustrated by ...
James W.H. Brown, Steven Roman
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Degenerate Sheffer sequences and λ-Sheffer sequences

Journal of Mathematical Analysis and Applications, 2021
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Kim, Dae San, Kim, Taekyun
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A note on the post quantum-Sheffer polynomial sequences

Forum Mathematicum
Abstract In this article, the post quantum analogue of Sheffer polynomial sequences is introduced using concepts of post quantum calculus. The series representation, recurrence relations, determinant expression and certain other properties of this class are established.
Subuhi Khan, Mehnaz Haneef
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Orthogonality Associated with Bessel-Type Sheffer Sequences with Q-Parameters

Mathematical Notes, 2022
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Riyasat, M., Nahid, T., Khan, S.
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Umbral calculus and Sheffer sequences of polynomials

Journal of Mathematical Physics, 2013
In this paper, we investigate some properties of Sheffer sequences of polynomials arising from umbral calculus. From these properties, we derive new and interesting identities between Sheffer sequences of polynomials. An application to normal ordering is presented.
Kim, Taekyun, Kim, Dae San, Mansour, Toufik, Rim, Seog-Hoon, Schork, Matthias   +4 more
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On supplementary formulas for Sheffer sequences

Aequationes mathematicae, 2015
The paper contains four theorems. In the first one, the author presents necessary and sufficient conditions for the Sheffer sequence to satisfy the supplementary formula. In the last three ones, characterizations of Bernoulli, Euler and poly-Bernoulli polynomials are given.
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A characterization of the exponential symmetric Sheffer sequences

Integral Transforms and Special Functions, 2020
A polynomial sequence (sn(x))n∈N is symmetric, or self-dual, if sn(m)=sm(n) for all m,n=0,1,2,….
Weiping Wang, Ke Zhang
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An algebraic approach to Sheffer polynomial sequences

Integral Transforms and Special Functions, 2013
A matrix approach to Sheffer polynomial sequences is proposed; in particular, two different determinantal forms of Sheffer sequences are given, the one as the function of a polynomial sequence of binomial type and the other as the function of the canonical base xi.
Francesco Aldo Costabile, Elisabetta Longo   +1 more
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Some New Identities Involving Sheffer–Appell Polynomial Sequences via Matrix Approach

Mediterranean Journal of Mathematics, 2019
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Marcellán, Francisco, Shadab, Mohd, Jabee, Saima   +2 more
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Symmetric Sheffer sequences and their applications to lattice path counting

Journal of Statistical Planning and Inference, 1996
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