Corpus ID: 235727655

Discrete orthogonal polynomials associated with Macdonald function

  title={Discrete orthogonal polynomials associated with Macdonald function},
  author={Semyon B. Yakubovich},
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. 


The Hypergeometric Approach to Integral Transforms and Convolutions
Preface. 1. Preliminaries. 2. Mellin Convolution Type Transforms with Arbitrary Kernels. 3. H- and G-Transforms. 4. The Generalized H- and G-Transforms. 5. The Generating Operators of GeneralizedExpand
Orthogonal Polynomials
In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.
Handbook of Special Functions: Derivatives, Integrals, Series and Other Formulas
The Derivatives. Limits. Indefinite Integrals. Definite Integrals. Infinite Series. The Connection Formulas. Representations of Hypergeometric Functions and the Meijer G Function.
Orthogonal polynomials for the weight $x^{\nu} \exp(-x - t/x)$
Date: May 14, 2021. 2000 Mathematics Subject Classification. 33C10, 42C05, 44A15 .
Higher Transcendental Functions,Vols
  • I and II, McGraw-Hill,
  • 1953
Orthogonal polynomials, Amer
  • Math. Soc. Colloq. Publ. XXIII,
  • 1939
Elementary Functions, Gordon and Breach, New York, London, 1986; Vol. II: Special Functions
  • 1990
Combinatorial identities, Wiley, New Yok
  • 1968