On the Asymptotics of the Meixner—Pollaczek Polynomials and Their Zeros
- 57 Downloads
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→∞ .
Unable to display preview. Download preview PDF.