Finite bivariate biorthogonal I - Konhauser polynomials

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-09-27 DOI:10.1016/j.cam.2025.117106

Esra Güldoğan Lekesi̇z , Bayram Çeki̇m , Mehmet Ali Özarslan

引用次数: 0

Abstract

In the present study, a finite set of biorthogonal polynomials in two variables, produced from Konhauser polynomials, is introduced. Some properties like Laplace transform, integral and operational representation, fractional calculus operators of this family are investigated. Also, we compute Fourier transform for this new set and discover a new family of finite biorthogonal functions with the help of Parseval’s identity. Further, in order to have semigroup property, we modify this finite set by adding two new parameters and construct fractional calculus operators. Thus, integral equation and integral operator are obtained for the modified version.

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有限二元双正交I - Konhauser多项式

本文介绍了由Konhauser多项式产生的二元双正交多项式的有限集。研究了该类算子的拉普拉斯变换、积分与运算表示、分数阶微积分算子等性质。同时，我们计算了这个新集合的傅里叶变换，并利用Parseval恒等式发现了一个新的有限双正交函数族。进一步，为了获得半群的性质，我们通过添加两个新参数来修改这个有限集，并构造分数阶微积分算子。从而得到了改进后的积分方程和积分算子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.