双变量拉盖尔多项式的量子(或 q$$ q$- )算子方程和相关偏微分方程,以及 q$$ q$-Hille-Hardy 型公式的应用

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS ACS Applied Bio Materials Pub Date : 2024-08-05 DOI:10.1002/mma.10328
Jian Cao, H. M. Srivastava, Yue Zhang
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引用次数: 0

摘要

基于包括(例如)-拉盖尔多项式在内的-数列和-多项式在数学和物理科学多个领域的广泛应用,我们非常重视涉及-拉盖尔多项式的方程和相关应用问题。本文的任务是从偏微分方程的角度出发,找出双变量拉盖尔多项式的一般运算方程及其展开问题。我们还给出了一些应用,包括一些 -Hille-Hardy 型公式。此外,我们还通过基于运算方程的技术,提出了双变量 - 拉盖尔多项式的罗杰斯型公式和 - 型生成函数。此外,我们还通过应用-运算方程,推导出涉及双变量-拉盖尔多项式的新的广义安德鲁斯-阿斯基积分和新的变换特征。
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Quantum (or q$$ q $$‐) operator equations and associated partial differential equations for bivariate Laguerre polynomials with applications to the q$$ q $$‐Hille‐Hardy type formulas
Based on the extensive application of the ‐series and ‐polynomials including (for example) the ‐Laguerre polynomials in several fields of the mathematical and physical sciences, we attach great importance to the equations and related application issues involving the ‐Laguerre polynomials. The mission of this paper is to find the general ‐operational equation together with the expansion issue of the bivariate ‐Laguerre polynomials from the perspective of ‐partial differential equations. We also give some applications including some ‐Hille‐Hardy type formulas. In addition, we present the Rogers‐type formulas and the ‐type generating functions for the bivariate ‐Laguerre polynomials by the technique based upon ‐operational equations. Moreover, we derive a new generalized Andrews‐Askey integral and a new transformation identity involving the bivariate ‐Laguerre polynomials by applying ‐operational equations.
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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