q-Bessel polynomials

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In mathematics, the q-Bessel polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.

Definition[edit]

The polynomials are given in terms of basic hypergeometric functions and the Pochhammer symbol by [1]

Orthogonality[edit]

[2]

Recurrence and difference relations[edit]

Rodrigues formula[edit]

Generating function[edit]

Relation to other polynomials[edit]

Gallery[edit]

QBessel function abs complex 3D Maple plot
QBessel function Im complex 3D Maple plot
QBessel function Re complex 3D Maple plot
QBessel function abs density Maple plot
QBessel function Im density Maple plot
QBessel function Re density Maple plot

References[edit]

  1. ^ Roelof Koekoek, Peter Lesky Rene Swarttouw,Hypergeometric Orthogonal Polynomials and their q-Analogues, p526 Springer 2010
  2. ^ Roelof p527