ON p, q-DIFFERENCE OPERATOR

Abstract

Abstract. In this paper, we define a p, q-difference operator and obtain an explicit formula which is used to express the p, q-analogue of the unified generalization of Stirling numbers and its exponential generating function in terms of the p, q-difference operator. Explicit formulas for the non-central q-Stirling numbers of the second kind and non-central q-Lah numbers are derived using the new q-analogue of Newton's interpolation formula. Moreover, a p, q-analogue of Newton's interpolation formula is established.

The q-Stirling numbers of the second kind and its applications

“…We also note that the expression Proposition 3.1 (1) and (3) were obtained in [3,10,11,21,28]. Proposition 3.1 (2) is due to Carlitz [4, (9)].…”