Identities Involving Generalized Harmonic Numbers and Other Special Combinatorial Sequences
نویسنده
چکیده
In this paper, we study the properties of the generalized harmonic numbersHn,k,r(α, β). In particular, by means of the method of coefficients, generating functions and Riordan arrays, we establish some identities involving the numbers Hn,k,r(α, β), Cauchy numbers, generalized Stirling numbers, Genocchi numbers and higher order Bernoulli numbers. Furthermore, we obtain the asymptotic values of some summations associated with the numbers Hn,k,r(α, β) by Darboux’s method and Laplace’s method.
منابع مشابه
Riordan arrays and harmonic number identities
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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