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Markov processes and a multiple generating function of product of generalized Laguerre polynomials
| Content Provider | Scilit |
|---|---|
| Author | Lee, Poh-Aun |
| Copyright Year | 1997 |
| Description | Journal: Journal of Physics A: General Physics From the spectral representation of the transition probability of birth-and-death processes, Karlin and McGregor show that the transition probability for the infinite server Markovian queue is in the form of a diagonal sum involving a product of Charlier polynomials. By using Meixner's bilinear generating formula for the Charlier polynomials and the Markov property, a multiple generating for the Charlier polynomials is deduced from the Chapman - Kolmogorov equation. The resulting formula possesses the same genre of a multiple generating function for the generalized Laguerre polynomials discussed by Messina and Paladimo, the explicit solution of which is recently given by the present author. |
| Related Links | http://iopscience.iop.org/article/10.1088/0305-4470/30/11/005/pdf |
| Ending Page | L377 |
| Page Count | 5 |
| Starting Page | L373 |
| ISSN | 00223689 |
| DOI | 10.1088/0305-4470/30/11/005 |
| Journal | Journal of Physics A: General Physics |
| Issue Number | 11 |
| Volume Number | 30 |
| Language | English |
| Publisher | IOP Publishing |
| Publisher Date | 1997-06-07 |
| Access Restriction | Open |
| Subject Keyword | Journal: Journal of Physics A: General Physics Applied Mathematics Mathematical Physics Generalized Laguerre Polynomials Transition Probability Generating Function Multiple Generating |
| Content Type | Text |
| Resource Type | Article |
