ON p, q-DIFFERENCE OPERATOR

Title & Authors
ON p, q-DIFFERENCE OPERATOR
Corcino, Roberto B.; Montero, Charles B.;

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