Corpus ID: 237605333

A modification of the Prudnikov and Laguerre polynomials

@inproceedings{Yakubovich2021AMO,
  title={A modification of the Prudnikov and Laguerre polynomials},
  author={Semyon B. Yakubovich},
  year={2021}
}
ABSTRACT. A two-parameter sequence of orthogonal polynomials {Pn(x;λ ,t)}n≥0 with respect to the weight function xα e−λxρν (xt), α > −1, λ ,t ≥ 0, ρν (x) = 2xKν (2 √ x), x > 0,ν ≥ 0, where Kν (z) is the modified Bessel function, is investigated. The case λ = 0 corresponds to the Prudnikov polynomials and t = 0 is related to the Laguerre polynomials. A special one-parameter case {Pn(x;1− t,t)}n≥0 , t ∈ [0,1] is analyzed as well. 

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