On the Stirling numbers associated with the meromorphic Weyl algebra

The generalized Stirling numbers introduced recently (Mansour and Schork, 2011 [5], Mansour et al., 2011 [6]) are considered in detail for the particular case s=2 corresponding to the meromorphic Weyl algebra. A combinatorial interpretation in terms of perfect matchings is given for these meromorphic Stirling numbers and the connection to Bessel functions is discussed. Furthermore, two related q-polynomial identities are derived.