Chihara–Ismail polynomials

In mathematics, the Chihara–Ismail polynomials are a family of orthogonal polynomials introduced by Chihara and Ismail (1982),[1] generalizing the van Doorn polynomials introduced by van Doorn (1981)[2] 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

  1. ^ Chihara, Theodore S.; Ismail, Mourad E.H. (December 1982). "Orthogonal polynomials suggested by a queueing model". Advances in Applied Mathematics. 3 (4): 441–462. doi:10.1016/S0196-8858(82)80017-1.
  2. ^ Van Doorn, Erik A. (June 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.


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