Volterra chain and Catalan numbers
Exactly Solvable and Integrable Systems
2019-03-29 v1 Combinatorics
Abstract
We consider the Cauchy problem for the Volterra chain with an initial condition equal to 0 in one node and 1 in the others. It is shown that this problem admits an exact solution in terms of the Bessel functions. The Taylor series arising here are related to the exponential generating function for Catalan numbers.
Cite
@article{arxiv.1810.13198,
title = {Volterra chain and Catalan numbers},
author = {V. E. Adler and A. B. Shabat},
journal= {arXiv preprint arXiv:1810.13198},
year = {2019}
}
Comments
4 pages, 2 figures