On generalized Stirling numbers

Title	On generalized Stirling numbers
Creator	蔡隆義 Tsai, Long-Yi
Contributor	應數系
Date	2002
Date Issued	11-Sep-2018 18:01:27 (UTC+8)
Summary	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
Type	conference

dc.contributor	應數系
dc.creator (作者)	蔡隆義	zh_TW
dc.creator (作者)	Tsai, Long-Yi	en_US
dc.date (日期)	2002
dc.date.accessioned	11-Sep-2018 18:01:27 (UTC+8)	-
dc.date.available	11-Sep-2018 18:01:27 (UTC+8)	-
dc.date.issued (上傳時間)	11-Sep-2018 18:01:27 (UTC+8)	-
dc.identifier.uri (URI)	http://nccur.lib.nccu.edu.tw/handle/140.119/120063	-
dc.description.abstract (摘要)	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.	en_US
dc.format.extent	161 bytes	-
dc.format.mimetype	text/html	-
dc.relation (關聯)	Analysis, combinatorics and computing, 397-417, Nova Sci. Publ., Hauppauge, NY, 2002
dc.title (題名)	On generalized Stirling numbers	en_US
dc.type (資料類型)	conference