We provide an interesting way to obtain the linear generating function for the classical discrete Charlier orthogonal polynomials by implementing what we entitle the 'Inverse Method'. This method transforms a given three-term recurrence relation into a differential equation, the solution of which is a linear generating function. To demonstrate the details of the procedure, we first apply the Inverse Method to the three-term recurrence relation that defines the Charlier polynomials. We then apply it to a new three-term recurrence relation, which is established via a certain connection between the Charlier polynomials and a variation of the Laguerre polynomials. The solution to each of these differential equations is the intended generating function.
|Original language||English (US)|
|Number of pages||8|
|Journal||Applied Mathematics E - Notes|
|State||Published - Oct 24 2013|
All Science Journal Classification (ASJC) codes
- Applied Mathematics