Corpus ID: 237605333

A modification of the Prudnikov and Laguerre polynomials

  title={A modification of the Prudnikov and Laguerre polynomials},
  author={Semyon B. Yakubovich},
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. 


Orthogonal Polynomials with Ultra-Exponential Weight Functions: An Explicit Solution to the Ditkin–Prudnikov Problem
New sequences of orthogonal polynomials with ultra-exponential weight functions are discovered. In particular, we give an explicit solution to the Ditkin–Prudnikov problem (1966). The 3-termExpand
Introduction to orthogonal polynomials
representations, parameterized by t > 0: J− en = √ n(t + n− 1) en−1, J+ en = √ (n + 1)(t + n) en+1, J0 en = (t + 2n)en. Want J− + J+ + cJ0 = X.
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
Introduction to the Theory of Fourier Integrals
SINCE the publication of Prof. Zygmund's “Trigonometric Series” in 1935, there has been considerable demand for another book dealing with trigonometric integrals. Prof. Titchmarsh's book meets thisExpand
Higher Transcendental Functions,Vols
  • I and II, McGraw-Hill,
  • 1953
Elementary Functions, Gordon and Breach, New York, London, 1986; Vol. II: Special Functions
  • 1990