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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.

A note on the convergence of Phillips operators by the sequence of functions via q-calculus

Kiliçman Adem, Ayman-Mursaleen Mohammad, Nasiruzzaman Md.

Demonstratio Mathematica

2022

Vol. 55, nr 1

615--633

The basic aim of this study is to include nonnegative real parameters to allow for approximation findings of the Stancu variant of Phillips operators. We concentrate on the uniform modulus of smoothness in a simple manner before moving on to the approximation in weighted Korovkin’s space. Our study’s goals and outcomes are to fully develop the uniformly approximated findings of Phillips operators. We determine the order of convergence in terms of Lipschitz maximal function and Peetre’s K-functional. In addition, the Voronovskaja-type theorem is also proved.

The CORDIC method of calculating the exponential function

Moroz L., Samotyy V.

Technical Transactions

2018

Vol. 115, iss. 4

119--126

This article presents a modern method of calculating the exponential function exp(x) based on the CORDIC iterative algorithm. The proposed solution is implemented in the form of a single iterative equation, which results in the simplification of the electronic version of this algorithm, thus reducing the cost of the device. It is important to point out that the accuracy of the calculation of the analysed function is not lost.

W artykule zaproponowano nowoczesną metodę obliczania funkcji eksponencjalnej exp(x) na bazie algorytmu iteracyjnego CORDIC. Przedstawione rozwiązanie jest realizowane w postaci jednego równania iteracyjnego, co prowadzi do uproszczenia wersji elektronicznej tego algorytmu i w wyniku zmniejsza koszt urządzenia. Należy podkreślić, że przy tym nie tracimy na dokładności obliczania badanej funkcji.

Exponential and Logarithmic Functions

Bittnerová D.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2003

Vol. 9

117--121

At the Technical University of Liberec, a new international Bachelor branch of studies was established for students of three states - Czech Republic, Poland, and Germany. These studies are intent on a management. We want to analyze students' understanding of one pivotal mathematical concept that plays a central role in advanced mathematics. We also want to compare a level of knowledge of these students from three different states. We aim at exponential and logarithmic functions because these concepts give students serious difficulties. In this report, we describe how students acquire an understanding of these functions by prescribing a set of mental constructions that students can make to develop their understanding of these concepts.