# ON p, q-DIFFERENCE OPERATOR

• Corcino, Roberto B. (Department of Mathematics Mindanao State University) ;
• Montero, Charles B. (Department of Mathematics Mindanao State University)
• Received : 2010.06.28
• Published : 2012.05.01
• 145 11

#### 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.

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