  Multiple Meixner polynomials are polynomials in one variable which satisfy
orthogonality relations with respect to $r>1$ different negative binomial
distributions (Pascal distributions). There are two kinds of multiple Meixner
polynomials, depending on the selection of the parameters in the negative
binomial distribution. We recall their definition and some formulas and give
generating functions and explicit expressions for the coefficients in the
nearest neighbor recurrence relation. Following a recent construction of Miki,
Tsujimoto, Vinet and Zhedanov (for multiple Meixner polynomials of the first
kind), we construct $r>1$ non-Hermitian oscillator Hamiltonians in $r$
dimensions which are simultaneously diagonalizable and for which the common
eigenstates are expressed in terms of multiple Meixner polynomials of the
second kind.
