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λ-q-Sheffer sequence and its applications

Kim Taekyun, Kim Dae San, Kim Hye Kyung

Demonstratio Mathematica

2022

Vol. 55, nr 1

843--865

Recently, Kim-Kim [J. Math. Anal. Appl. 493 (2021), no. 1] introduced the degenerate Sheffer sequence and λ-Sheffer sequence. The purpose of this article is to study λ-q-Sheffer sequence and the degenerate q-Sheffer sequence, which are derived from the view point of degenerate umbral calculus and investigate some properties related to those sequences. In addition, we give some new identities associated with q-special polynomials arising from our investigation.

Euler approximations can destroy unbounded solutions

Guy R. T., Misiurewicz M.

Fasciculi Mathematici

2010

Nr 44

43-52

We show that there are ordinary differential equations in Rd with unbounded solutions, for which the difference equations obtained by using the forward Euler method have all solutions bounded.