Multivariate Pascal Polynomials of Order K with Probability Applications

Demetrios L. Antzoulakos and Andreas N. Philippou

A chapter in Applications of Fibonacci Numbers, 1999, pp 27-41 from Springer

Abstract: Abstract For any fixed positive integer k, let C k(n, m) be the entry at the intersection of row n (n ≥ 0) and column m (m ≥ 0) in the Pascal triangle of order k, viz., T k. Then $$C_{1}(n,0)=1 \text{ for} n \geq 0 \text{ and} C_{1}(n,m)=0 \text{ for} m\geq 1$$ , and for k ≥ 2, C k(0,0) = 1, C k(0,m) = 0 for m ≥ 1, and 1 $$ {{C}_{k}}(n,m) = \left\{ {\begin{array}{*{20}{c}} {\sum\limits_{{i = 1}}^{m} {{{C}_{k}}} (n - 1,m - i), 0 \leqslant m \leqslant k - 1{\text{ and}} n \geqslant 1} \hfill \\ {\sum\limits_{{i = 0}}^{{k - 1}} {{{C}_{k}}} (n - 1,m - i), m \geqslant k{\text{ and}} n \geqslant 1.} \hfill \\ \end{array} } \right. $$ .

Keywords: 11B65; 62E15; 11B39 (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1007/978-94-011-4271-7_3

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