(r， β)-Stirling矩阵的线性代数

IF 1 Q1 MATHEMATICS European Journal of Pure and Applied Mathematics Pub Date : 2023-10-30 DOI:10.29020/nybg.ejpam.v16i4.4854

Genevieve B. Engalan, Mary Joy Latayada

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摘要

本文建立了$(r， \beta)$-Stirling矩阵的线性代数。在此过程中，本文导出了各种恒等式，如它的因式分解及其与Pascal矩阵和第二类Stirling矩阵的关系。此外，本文还提出了Vandermonde矩阵的一个自然推广，可用于等差数列的连续幂和的研究和求值。

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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The Linear Algebra of (r, β)-Stirling Matrices

This paper establishes the linear algebra of the $(r, \beta)$-Stirling matrix. Along the way, this paper derives various identities, such as its factorization and relationship to the Pascal matrix and the Stirling matrix of the second kind. Additionally, this paper develops a natural extension of the Vandermonde matrix, which can be used to study and evaluate successive power sums of arithmetic progressions.

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