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The linear algebra of the generalized Pascal functional matrix

โœ Scribed by M. Bayat; H. Teimoori

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
91 KB
Volume
295
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

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 n P 0 , and obtain several important combinatorial identities.

๐Ÿ“œ SIMILAR VOLUMES

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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

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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.