On generalizations of Stirling numbers and some well-known matrices. (English) Zbl 07833969
Summary: We introduce a generalization of the Stirling numbers of the first kind and the second kind. By arranging these numbers into matrices, we generalize the Stirling matrices of the first kind and the second kind investigated by G.-S. Cheon and J.-S. Kim [Linear Algebra Appl. 329, No. 1–3, 49–59 (2001; Zbl 0988.05009)]. Furthermore, we introduce generalizations of the Pascal matrix and the symmetric Pascal matrix with two real arguments, and generalize earlier results related to the Pascal matrices, Stirling matrices and matrices involving Bell numbers.
MSC:
| 11B73 | Bell and Stirling numbers |
| 05A10 | Factorials, binomial coefficients, combinatorial functions |
| 15A23 | Factorization of matrices |
| 15A24 | Matrix equations and identities |
| 15B05 | Toeplitz, Cauchy, and related matrices |
| 33C05 | Classical hypergeometric functions, \({}_2F_1\) |
Keywords:
Pascal matrix; Stirling numbers; Stirling matrix; generalized hypergeometric function; Cholesky factorization; Bell numbersCitations:
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