On the q-Charlier Multiple Orthogonal Polynomials Articles uri icon

publication date

  • March 2015

start page

  • 1

end page

  • 14

issue

  • 26

volume

  • 11

international standard serial number (ISSN)

  • 1815-0659

abstract

  • We introduce a new family of special functions, namely q-Charlier multiple orthogonal polynomials. These polynomials are orthogonal with respect to q-analogues of Poisson distributions. We focus our attention on their structural properties. Raising and lowering operators as well as Rodrigues-type formulas are obtained. An explicit representation in terms of a q-analogue of the second of Appell's hypergeometric functions is given. A high-order linear q-difference equation with polynomial coefficients is deduced. Moreover, we show how to obtain the nearest neighbor recurrence relation from some difference operators involved in the Rodrigues-type formula.

keywords

  • multiple orthogonal polynomials; hermite-padé approximation; difference equations; classical orthogonal polynomials of a discrete variable; charlier polynomials; q-polynomials