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|Title:||On generalized Stirling numbers|
|Issue Date:||2018-09-11 18:01:27 (UTC+8)|
|Abstract:||Let (z|α)n=z(z−α)⋯(z−nα+α). A "Stirling type pair''|
is defined by means of
(t|α)n=∑k=0nS1(n,k)(t−r|β)k,(t|β)n=∑k=0nS2(n,k)(t+r|α)k. By specializing the parameters α, β and r, one can obtain the Stirling numbers and various generalizations of the Stirling numbers. These definitions are not new; for example, S1(n,k) and S2(n,k) were defined and studied in [L. C. Hsu and H. Q. Yu, Appl. Math. J. Chinese Univ. Ser. B 12 (1997), no. 2, 225–232; MR1460101], where two of the generating functions in the present paper are given. See also [L. C. Hsu and P. J.-S. Shiue, Adv. in Appl. Math. 20 (1998), no. 3, 366–384; MR1618435], where many properties of S1 and S2 are worked out. Evidently, the paper under review is mainly concerned with proving generating functions and asymptotic expansions.
|Relation:||Analysis, combinatorics and computing, 397-417, Nova Sci. Publ., Hauppauge, NY, 2002|
|Appears in Collections:||[應用數學系] 會議論文|
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