Existence of a pair of new recurrence relations for the MeixnerPollaczek polynomials
E. I. Jafarov, A. M. Jafarova, S. M. Nagiyev
We report on existence of pair of new recurrence relations (or difference equations) for the MeixnerPollaczek polynomials.
Proof of the correctness of these difference equations is also presented. Next, we found that subtraction of the forward shift operator for
the MeixnerPollaczek polynomials from one of these recurrence relations leads to the difference equation for the MeixnerPollaczek polynomials
generated via cosh difference differentiation operator. Then, we show that, under the limit φ
→ 0, new recurrence relations for the
MeixnerPollaczek polynomials recover pair of the known recurrence relations for the generalized Laguerre polynomials. At the end, we introduced differentiation
formula, which expresses MeixnerPollaczek polynomials with parameters
λ > 0 and 0 < φ < π via generalized Laguerre polynomials.
Tbilisi Mathematical Journal, Vol. 11(3) (2018), pp. 2939
