Simplifying coefficients in differential equations for generating function of Catalan numbers

被引：10
|
作者：
Qi, Feng [1 ,2 ,3 ]
Yao, Yong-Hong [3 ]
机构：
[1] Henan Polytech Univ, Inst Math, Jiaozuo 454010, Henan, Peoples R China
[2] Inner Mongolia Univ Nationalities, Coll Math, Tongliao 028043, Inner Mongolia, Peoples R China
[3] Tianjin Polytech Univ, Sch Math Sci, Tianjin 300387, Peoples R China
来源：
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE | 2019年 / 13卷 / 01期
关键词：
Simplifying; coefficient; nonlinear ordinary differential equation; generating function; Catalan number; Faa di Bruno formula; Bell polynomial of the second kind; inversion theorem; BELL POLYNOMIALS; SPECIAL VALUES; FAMILY; FORMULAS;
D O I：
10.1080/16583655.2019.1663782
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In the paper, by the Faa di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients in two families of nonlinear ordinary differential equations for the generating function of the Catalan numbers.
引用
收藏
页码：947 / 950
页数：4
相关论文
共 50 条
  • [21] Differential equations arising from the generating function of general modified degenerate Euler numbers
    Kim, Tae Kyun
    Kim, Dae San
    Kwon, Hyuck In
    Seo, Jong Jin
    ADVANCES IN DIFFERENCE EQUATIONS, 2016,
  • [22] Differential equations arising from the generating function of general modified degenerate Euler numbers
    Tae Kyun Kim
    Dae San Kim
    Hyuck In Kwon
    Jong Jin Seo
    Advances in Difference Equations, 2016
  • [23] AN APPLICATION OF GENERATING FUNCTION TO DIFFERENTIAL EQUATIONS
    NEWTON, TA
    AMERICAN MATHEMATICAL MONTHLY, 1961, 68 (03): : 242 - &
  • [24] GENERATING TREES AND THE CATALAN AND SCHRODER NUMBERS
    WEST, J
    DISCRETE MATHEMATICS, 1995, 146 (1-3) : 247 - 262
  • [25] Catalan triangle numbers and binomial coefficients
    Lee, Kyu-Hwan
    Oh, Se-jin
    REPRESENTATIONS OF LIE ALGEBRAS, QUANTUM GROUPS AND RELATED TOPICS, 2018, 713 : 165 - 185
  • [26] A SIMPLE FORM FOR COEFFICIENTS IN A FAMILY OF ORDINARY DIFFERENTIAL EQUATIONS RELATED TO THE GENERATING FUNCTION OF THE LEGENDRE POLYNOMIALS
    Qi, Feng
    ADVANCES AND APPLICATIONS IN MATHEMATICAL SCIENCES, 2018, 17 (11): : 693 - 700
  • [27] IDENTITIES FOR THE CATALAN GENERATING FUNCTION
    BINZ, JC
    AMERICAN MATHEMATICAL MONTHLY, 1995, 102 (04): : 365 - 365
  • [28] Methods for Simplifying Differential Equations
    Aldossari, Shayea
    van Hoeij, Mark
    ACM COMMUNICATIONS IN COMPUTER ALGEBRA, 2019, 53 (03): : 93 - 95
  • [29] Series with Central Binomial Coefficients,Catalan Numbers,and Harmonic Numbers
    Boyadzhiev, Khristo N.
    JOURNAL OF INTEGER SEQUENCES, 2012, 15 (01)
  • [30] On the Euler function of the Catalan numbers
    Luca, Florian
    Stanica, Pantelimon
    JOURNAL OF NUMBER THEORY, 2012, 132 (07) : 1404 - 1424
12345