## Abstract

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) |
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Pages (from-to) | 60-67 |

Number of pages | 8 |

Journal | Applied Mathematics E - Notes |

Volume | 13 |

State | Published - Oct 24 2013 |

## All Science Journal Classification (ASJC) codes

- Applied Mathematics