Q-Charlier polynomials explained

In mathematics, the q-Charlier polynomials^[1] are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. give a detailed list of their properties.

Definition

The polynomials are given in terms of the basic hypergeometric function by

\displaystyle C ^{- x} _{n(q} ;a;q) = {} _{2\phi} ^{- n} ^{1 (q} ,q ^{-x} ; 0 ;q, - q ^{n+1} /a).

References

• • • • Sadjang . Patrick Njionou . Moments of Classical Orthogonal Polynomials . Ph.D. . Universität Kassel . 10.1.1.643.3896 .

Notes and References

1. There are similar named polynomials named alternative q-Charlier polynomials K _{n(x;a;q)} which is another name for q-Bessel polynomials.