English

On a functional-difference equation of Runyon, Morrison, Carlitz, and Riordan

Combinatorics 2007-05-23 v1

Abstract

A certain functional-difference equation that Runyon encountered when analyzing a queuing system was solved in a combined effort of Morrison, Carlitz, and Riordan. We simplify that analysis by exclusively using generating functions, in particular the kernel method, and the Lagrange inversion formula.

Cite

@article{arxiv.math/0103149,
  title  = {On a functional-difference equation of Runyon, Morrison, Carlitz, and Riordan},
  author = {Helmut Prodinger},
  journal= {arXiv preprint arXiv:math/0103149},
  year   = {2007}
}

Comments

Avoid recursions, use generating functions

R2 v1 2026-07-22T16:37:49.368Z