Generalized Pascal matrix and recurrence sequences
โ Scribed by Zhizheng Zhang; Tianming Wang
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 485 KB
- Volume
- 283
- Category
- Article
- ISSN
- 0024-3795
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๐ SIMILAR VOLUMES
In this paper we generalize Pascal's matrix by deยฎning the polynomials ``Factorial Binomial''. Then using this generalization, we introduce a two-variable Pascal's matrix and state its related theorems and prove them. Finally we introduce Pascal's functional matrix associated with a sequence a f n g
The extended generalized Pascal matrix can be represented in two different ways: as a lower triangular matrix d~n [x, y] or as a symmetric ~.[x, y]. These matrices generalize Pn[X], Qn[X], and Rn[X], which are defined by Zhang and by Call and Velleman. A product formula for dp.[ x, y] has been found
The R. x n generalized Pascal matrix P(t) whose elements are related to the hypergeometric function zFr(a, b; c; Z) is presented and the Cholesky decomposition of P(t) is obtained.