Chihara–Ismail polynomials

In mathematics, the Chihara–Ismail polynomials are a family of orthogonal polynomials introduced by Chihara and Ismail (1982), generalizing the van Doorn polynomials introduced by van Doorn (1981) and the Karlin–McGregor polynomials. They have a rather unusual measure, which is discrete except for a single limit point at 0 with jump 0, and is non-symmetric, but whose support has an infinite number of both positive and negative points.

References

• Chihara, Theodore Seio; Ismail, Mourad E. H. (1982), "Orthogonal polynomials suggested by a queueing model", Advances in Applied Mathematics, 3 (4): 441–462, doi:10.1016/S0196-8858(82)80017-1, ISSN 0196-8858, MR 682630
• van Doorn, Erik A. (1981), "The transient state probabilities for a queueing model where potential customers are discouraged by queue length", Journal of Applied Probability, 18 (2): 499–506, doi:10.2307/3213296, ISSN 0021-9002, MR 611792