# Discrete orthogonal polynomials associated with Macdonald function

@inproceedings{Yakubovich2021DiscreteOP, title={Discrete orthogonal polynomials associated with Macdonald function}, author={Semyon B. Yakubovich}, year={2021} }

New sequences of discrete orthogonal polynomials associated with the modified Bessel function Kμ (z) or Macdonald function are considered. The corresponding weight function is λ ρk+ν+1(t)/k!, where k ∈ N0, t ≥ 0, ν > −1, 0 < λ < 1, ρμ (z) = 2zKμ (2 √ z). The limit case t = 0 corresponds to the Meixner polynomials. Various properties, differential-difference recurrence relations are established. The modified sequence of polynomials with the weight λ ρk+ν+1(λt)/k! is investigated as well.

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