Henry W. GOULD,何天晓.Characterization of $(c)$-Riordan Arrays, Gegenbauer-Humbert-Type Polynomial Sequences, and $(c)$-Bell Polynomials[J].数学研究及应用,2013,33(5):505~527
Characterization of $(c)$-Riordan Arrays, Gegenbauer-Humbert-Type Polynomial Sequences, and $(c)$-Bell Polynomials
Characterization of $(c)$-Riordan Arrays, Gegenbauer-Humbert-Type Polynomial Sequences, and $(c)$-Bell Polynomials
投稿时间:2012-12-07  最后修改时间:2013-02-18
DOI:10.3770/j.issn:2095-2651.2013.05.001
中文关键词:  Riordan arrays  $(c)$-Riordan arrays  $A$-sequence  $Z$-sequence  $(c)$-Bell polynomials  $(c)$-hitting-time subgroup.
英文关键词:Riordan arrays  $(c)$-Riordan arrays  $A$-sequence  $Z$-sequence  $(c)$-Bell polynomials  $(c)$-hitting-time subgroup.
基金项目:
作者单位
Henry W. GOULD Department of Mathematics, West Virginia University, Morgantown, WV $26505$, USA 
何天晓 Department of Mathematics, Illinois Wesleyan University, Bloomington, IL 61702, USA 
摘要点击次数: 2065
全文下载次数: 1444
中文摘要:
      Here presented are the definitions of $(c)$-Riordan arrays and $(c)$-Bell polynomials which are extensions of the classical Riordan arrays and Bell polynomials. The characterization of $(c)$-Riordan arrays by means of the $A$- and $Z$-sequences is given, which corresponds to a horizontal construction of a $(c)$-Riordan array rather than its definition approach through column generating functions. There exists a one-to-one correspondence between Gegenbauer-Humbert-type polynomial sequences and the set of $(c)$-Riordan arrays, which generates the sequence characterization of Gegenbauer-Humbert-type polynomial sequences. The sequence characterization is applied to construct readily a $(c)$-Riordan array. In addition, subgrouping of $(c)$-Riordan arrays by using the characterizations is discussed. The $(c)$-Bell polynomials and its identities by means of convolution families are also studied. Finally, the characterization of $(c)$-Riordan arrays in terms of the convolution families and $(c)$-Bell polynomials is presented.
英文摘要:
      Here presented are the definitions of $(c)$-Riordan arrays and $(c)$-Bell polynomials which are extensions of the classical Riordan arrays and Bell polynomials. The characterization of $(c)$-Riordan arrays by means of the $A$- and $Z$-sequences is given, which corresponds to a horizontal construction of a $(c)$-Riordan array rather than its definition approach through column generating functions. There exists a one-to-one correspondence between Gegenbauer-Humbert-type polynomial sequences and the set of $(c)$-Riordan arrays, which generates the sequence characterization of Gegenbauer-Humbert-type polynomial sequences. The sequence characterization is applied to construct readily a $(c)$-Riordan array. In addition, subgrouping of $(c)$-Riordan arrays by using the characterizations is discussed. The $(c)$-Bell polynomials and its identities by means of convolution families are also studied. Finally, the characterization of $(c)$-Riordan arrays in terms of the convolution families and $(c)$-Bell polynomials is presented.
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