Generalized Stirling Numbers, Convolution Formulae and p, q-Analogues
نویسندگان
چکیده
منابع مشابه
Rook Theory, Generalized Stirling Numbers and (p, q)-Analogues
In this paper, we define two natural (p, q)-analogues of the generalized Stirling numbers of the first and second kind S(α, β, r) and S(α, β, r) as introduced by Hsu and Shiue [17]. We show that in the case where β = 0 and α and r are nonnegative integers both of our (p, q)-analogues have natural interpretations in terms of rook theory and derive a number of generating functions for them. We al...
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متن کاملA q-ANALOGUE OF GENERALIZED STIRLING NUMBERS
We investigate a kind of q-analogue which involves a unified generalization of Stirling numbers as a limiting case with q→1. Some basic properties and explicit formulas will be derived, and certain applications related to previously known results will be discussed.
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In this paper, we establish several properties of the unified generalized Stirling numbers of the first kind, and the Jacobi-Stirling numbers of the first kind, by means of the convolution principle of sequences. Obtained results include generalized Vandermonde convolution for the unified generalized Stirling numbers of the first kind, triangular recurrence relation for general Stirling-type nu...
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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 1995
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-1995-027-x