A simple proof for an integral representation of the Catalan numbers that makes use of an ordinary generating function approach and relies on essentially nothing beyond elementary integral calculus is presented. Application of the integral representation given is then made in the evaluation of a family of infinite sums consisting of products between the central binomial coeffi cient and the bicentral binomial coeffi cient.
|Original language||English (US)|
|Number of pages||7|
|Journal||Applied Mathematics E - Notes|
|State||Published - Jan 1 2022|
ASJC Scopus subject areas
- Applied Mathematics