Some identities on Catalan numbers and hypergeometric functions via Catalan matrix power

Some identities on Catalan numbers and hypergeometric functions via Catalan matrix power

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Article ID: iaor20115678
Volume: 217
Issue: 22
Start Page Number: 9122
End Page Number: 9132
Publication Date: Jul 2011
Journal: Applied Mathematics and Computation
Authors:
Keywords: geometric modelling, linear algebra
Abstract:

In this paper we use the Catalan matrix power as a tool for deriving identities involving Catalan numbers and hypergeometric functions. For that purpose, we extend earlier investigated relations between the Catalan matrix and the Pascal matrix by inserting the Catalan matrix power and particulary the squared Catalan matrix in those relations. We also pay attention to some relations between Catalan matrix powers of different degrees, which allows us to derive the simplification formula for hypergeometric function 3 F 2, as well as the simplification formula for the product of the Catalan number and the hypergeometric function 3 F 2. Some identities involving Catalan numbers, proved by the non‐matrix approach, are also given.

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