Discrete orthogonal polynomials associated with Macdonald function
Abstract
New sequences of discrete orthogonal polynomials associated with the modified Bessel function $K_\mu(z)$ or Macdonald function are considered. The corresponding weight function is $\lambda^k \rho_{k+\nu+1}(t)/ k!$, where $\ k \in \mathbb{N}_0, \ t \ge 0,\ \nu > 1,\ 0 < \lambda < 1,\ \rho_{\mu}(z) = 2 z^{\mu/2} K_\mu\left( 2\sqrt z\right)$. The limit case $t=0$ corresponds to the Meixner polynomials. Various properties, differentialdifference recurrence relations are established. The modified sequence of polynomials with the weight $\lambda^k \rho_{k+\nu+1}(\lambda t)/ k! $ is investigated as well.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.00943
 Bibcode:
 2021arXiv210700943Y
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 33C10;
 42C05;
 44A15