Asymptotics of the associated Pollaczek polynomials
Asymptotics of the associated Pollaczek polynomials
In this note, we investigate the large-$n$ behavior of the associated Pollaczek polynomials $P_{n}^{\lambda }\left (z;a,b,c\right )$. These polynomials involve four real parameters $\lambda$, $a$, $b$, and $c$, in addition to the complex variable $z$. Asymptotic formulas are derived for these polynomials, when $z$ lies in the complex plane bounded …