Generalized harmonic numbers with Riordan arrays
نویسندگان
چکیده
منابع مشابه
Generalized Riordan arrays
In this paper, we generalize the concept of Riordan array. A generalized Riordan array with respect to cn is an infinite, lower triangular array determined by the pair (g(t), f(t)) and has the generic element dn,k = [t/cn]g(t)(f(t))/ck, where cn is a fixed sequence of non-zero constants with c0 = 1. We demonstrate that the generalized Riordan arrays have similar properties to those of the class...
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A Riordan array is an infinite complex matrix (ars) of a certain type (see below for exact definitions). The Riordan array formalism has been much used recently to study combinatorial questions in analysis of algorithms and other areas. Most work has been concerned with “exact” results. In this article we discuss asymptotics of such arrays. We apply general machinery for deriving asymptotics of...
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Let the numbers P (r, n, k) be defined by P (r, n, k) := Pr ( H n −H (1) k , · · · , H (r) n −H (r) k ) , where Pr(x1, · · · , xr) = (−1)Yr(−0!x1,−1!x2, · · · ,−(r− 1)!xr) and Yr are the exponential complete Bell polynomials. By observing that the numbers P (r, n, k) generate two Riordan arrays, we establish several general summation formulas, from which series of harmonic number identities are...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2008
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2007.08.011