Hankel transform of a sequence obtained by series reversion II - aerating transforms

Details Hankel transform of a sequence obtained by series reversion II - aerating transforms Hankel transform of a sequence obtained by series reversion II - aerating transforms

2011-12-07

arxiv.org/abs/1112.1656v1

Mathematics

Combinatorics

Scientific paper

This paper provides the connection between the Hankel transform and aerating transforms of a given integer sequence. Results obtained are used to establish a completely different Hankel transform evaluation of the series reversion of a certain rational function $Q(x)$ and shifted sequences, recently published in our paper \cite{part1}. For that purpose, we needed to evaluate the Hankel transforms of the sequences $\seqn{\alpha^2 C_n-\beta C_{n+1}}$ and $\seqn{\alpha^2 C_{n+1}-\beta C_{n+2}}$, where $C=\seqn{C_n}$ is the well-known sequence of Catalan numbers. This generalizes the results of Cvetkovi\' c, Rajkovi\'c and Ivkovi\'c \cite{CRI}. Also, we need the evaluation of Hankel-like determinants whose entries are Catalan numbers $C_n$ and which is based on the recent results of Krattenthaler \cite{krattCat}. The results obtained are general and can be applied to many other Hankel transform evaluations.

Affiliated with

Also associated with

No associations

Rating

Hankel transform of a sequence obtained by series reversion II - aerating transforms 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 Hankel transform of a sequence obtained by series reversion II - aerating transforms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hankel transform of a sequence obtained by series reversion II - aerating transforms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-598739