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.
|Number of pages
|Applied Mathematics E - Notes
|Published - 2013
All Science Journal Classification (ASJC) codes
- Applied Mathematics