Asymptotic Expansions of Central Binomial Coefficents and Catalan Numbers

被引：0
|
作者：
Elezovic, Neven [1 ]
机构：
[1] Univ Zagreb, Fac Elect Engn & Comp, Unska 3, Zagreb 10000, Croatia
来源：
JOURNAL OF INTEGER SEQUENCES | 2014年 / 17卷 / 02期
关键词：
binomia coefficient; catalan number; asymptotic expension; gamma function;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give systematic view of the asymptotic expension of two well-known sequences,the central binomial coefficients and the Catalan numbers. The main Point is Explanation of the nature of the best shift in variable n,in order to obtain "nice" asymptotic expansions.we also give a complete asymptotic expansion of partial sums of these sequences.
引用
收藏
页数：14
相关论文
共 50 条
  • [31] Combinatorial Interpretations of Lucas Analogues of Binomial Coefficients and Catalan Numbers
    Bennett, Curtis
    Carrillo, Juan
    Machacek, John
    Sagan, Bruce E.
    ANNALS OF COMBINATORICS, 2020, 24 (03) : 503 - 530
  • [32] On sums of binomial coefficients involving Catalan and Delannoy numbers modulo
    Mao, Guo-Shuai
    RAMANUJAN JOURNAL, 2018, 45 (02): : 319 - 330
  • [33] Combinatorial Interpretations of Lucas Analogues of Binomial Coefficients and Catalan Numbers
    Curtis Bennett
    Juan Carrillo
    John Machacek
    Bruce E. Sagan
    Annals of Combinatorics, 2020, 24 : 503 - 530
  • [34] ASYMPTOTIC EXPANSIONS FOR THE STIRLING NUMBERS OF THE FIRST KIND
    HWANG, HK
    JOURNAL OF COMBINATORIAL THEORY SERIES A, 1995, 71 (02) : 343 - 351
  • [35] Taylor expansions for the generating function of Catalan-like numbers
    Liu, Lily Li
    Li, Xiaoli
    COGENT MATHEMATICS, 2016, 3
  • [36] On asymptotic expansions in the domain of large deviations for binomial and Poisson distributions
    Timashev, AN
    THEORY OF PROBABILITY AND ITS APPLICATIONS, 1999, 43 (01) : 89 - 98
  • [37] ON CERTAIN SERIES EXPANSIONS OF THE SINE FUNCTION: CATALAN NUMBERS AND CONVERGENCE
    Larcombe, Peter J. .
    O'Neill, Sam T. .
    Fennessey, Eric J. .
    FIBONACCI QUARTERLY, 2014, 52 (03): : 236 - 242
  • [38] POLYNOMIAL FORMS FOR ALTERNATING SUMS OF PRODUCTS OF BINOMIAL-CATALAN NUMBERS
    Gauthier, N.
    FIBONACCI QUARTERLY, 2012, 50 (01): : 62 - 67
  • [39] ASYMPTOTIC EXPANSIONS IN CENTRAL LIMIT THEOREM
    GALSTYAN, FN
    THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1971, 16 (03): : 528 - &
  • [40] ASYMPTOTIC EXPANSIONS IN CENTRAL LIMIT THEOREM
    ROZOVSKII, LV
    TEORIYA VEROYATNOSTEI I YEYE PRIMENIYA, 1975, 20 (04): : 810 - 820
12345