Abstract
Excerpt from the abstract:
It is known that the ( m, r )-central coefficient triangles of any Riordan array are also Riordan arrays. In this paper, for a Riordan array G = ( d, h ) with h (0) = 0 and d (0), h ′ (0) 6≠ 0, we obtain the generating function of its ( m, r )-central coefficients and give an explicit representation for the (m, r)-central Riordan array G (m,r) in terms of the Riordan array G . Meanwhile, the algebraic structures of the ( m, r )-central Riordan arrays are also investigated, such as their decompositions, their inverses, and their recessive expressions in terms of m and r. As applications, we determine the ( m, r )-central Riordan arrays of the Pascal matrix and other Riordan arrays, from which numerous identities are constructed by a uniform approach.
Original language | American English |
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Journal | Czechoslovak Mathematical Journal |
Volume | 67 |
DOIs | |
State | Published - Oct 2017 |
Keywords
- Catalan matrix
- Fuss-Catalan number
- Pascal matrix
- Riordan array
- central Riordan array
- central coefficient
- generating function
Disciplines
- Applied Mathematics
- Mathematics