Abstract.
An infinite asymptotic expansion is derived for the Meixner—Pollaczek polynomials M n (nα;δ, η) as n→∞ , which holds uniformly for -M≤α≤ M , where M can be any positive number. This expansion involves the parabolic cylinder function and its derivative. If α n, s denotes the s th zero of M n (nα;δ, η) , counted from the right, and if α˜ n,s denotes its s th zero counted from the left, then for each fixed s , three-term asymptotic approximations are obtained for both α n,s and α˜ n,s as n→∞ .
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December 28, 1998. Date revised: June 4, 1999. Date accepted: September 6, 1999.
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Li, X., Wong, R. On the Asymptotics of the Meixner—Pollaczek Polynomials and Their Zeros. Constr. Approx. 17, 59–90 (2001). https://doi.org/10.1007/s003650010009
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DOI: https://doi.org/10.1007/s003650010009