Recurrence relations for polynomial sequences via Riordan matrices

By Ana Luzón, M. A. Mor'on. 2009

50 citations recorded by the source corpus.

We give recurrence relations for any family of generalized Appell polynomials unifying so some known recurrences for many classical sequences of polynomials. Our main tool to get our goal is the Riordan group. We use the product of Riordan matrices to interpret some relationships between different polynomial families. Moreover using the Hadamard product of series we get a general recurrence relation for the polynomial sequences associated to the so called generalized umbral calculus.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0ebe39abb237d85293f7be5cb8f09a22c71f408a

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In Algebra and Number Theory

1. Paul Barry
2. Aoife Hennessy
3. Donatella Merlini
4. Renzo Sprugnoli
5. Ana Luzón
6. M. A. Mor'on

In Discrete Mathematics and Combinatorics

1. Paul Barry
2. Aoife Hennessy
3. Donatella Merlini
4. Renzo Sprugnoli
5. Ana Luzón
6. M. A. Mor'on

In Mathematical Physics

1. Paul Barry
2. Aoife Hennessy
3. Donatella Merlini
4. Renzo Sprugnoli
5. Ana Luzón
6. M. A. Mor'on

Citations in the corpus

• Meixner-Type Results for Riordan Arrays and Associated Integer Sequences (2010, methodology): “Theorem 5 of [19] now yields the required form of the three-term recurrence for the associated polynomials with coefficient array L−1.”
• Identities induced by Riordan arrays (2012, methodology): “This construction was used in [8, 9] for different purposes.”