Riordan arrays and applications via the classical umbral calculus

Details Riordan arrays and applications via the classical umbral calculus Riordan arrays and applications via the classical umbral calculus

2011-03-30

arxiv.org/abs/1103.5879v1

Mathematics

Combinatorics

20 pages

Scientific paper

We use the classical umbral calculus to describe Riordan arrays. Here, a Riordan array is generated by a pair of umbrae, and this provides efficient proofs of several basic results of the theory such as the multiplication rule, the recursive properties, the fundamental theorem and the connection with Sheffer sequences. In particular, we show that the fundamental theorem turns out to be a reformulation of the umbral Abel identity. As an application, we give an elementary approach to the problem of extending integer powers of Riordan arrays to complex powers in such a way that additivity of the exponents is preserved. Also, ordinary Riordan arrays are studied within the classical umbral perspective and some combinatorial identities are discussed regarding Catalan numbers, Fibonacci numbers and Chebyshev polynomials.

Affiliated with

Also associated with

No associations

Rating

Riordan arrays and applications via the classical umbral calculus does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Riordan arrays and applications via the classical umbral calculus, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Riordan arrays and applications via the classical umbral calculus will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-568233