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Title: On generalized Stirling numbers
Authors: 蔡隆義
Tsai, Long-Yi
Contributors: 應數系
Date: 2002
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''
{S1(n,k),S2(n,k)}={S(n,k;α,β,r), S(n,k;β,α,−r)}
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
Data Type: conference
Appears in Collections:[應用數學系] 會議論文

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