| Characterization of $(c)$-Riordan Arrays, Gegenbauer-Humbert-Type Polynomial Sequences, and $(c)$-Bell Polynomials |
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| 作者姓名： | Henry W. GOULD 何天晓 |
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| 作者单位： | Department of Mathematics, West Virginia University, Morgantown, WV $26505$, USA;Department of Mathematics, Illinois Wesleyan University, Bloomington, IL 61702, USA |
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| 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 GegenbauerHumbert-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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| 关 键 词： | Riordan arrays (c)-Riordan arrays A-sequence Z-sequence (c)-Bell polynomials (c)-hitting-time subgroup. |
| 收稿时间： | 2012/12/7 0:00:00 |
| 修稿时间： | 2013/2/18 0:00:00 |
Characterization of $(c)$-Riordan Arrays, Gegenbauer-Humbert-Type Polynomial Sequences, and $(c)$-Bell Polynomials |
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| Henry W. GOULD and Tianxiao HE.Characterization of $(c)$-Riordan Arrays, Gegenbauer-Humbert-Type Polynomial Sequences, and $(c)$-Bell Polynomials[J].Journal of Mathematical Research with Applications,2013,33(5):505-527. |
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| Authors: | Henry W GOULD and Tianxiao HE |
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| Institution: | Department of Mathematics, West Virginia University, Morgantown, WV $26505$, USA;Department of Mathematics, Illinois Wesleyan University, Bloomington, IL 61702, USA |
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| Abstract: | 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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| Keywords: | Riordan arrays $(c)$-Riordan arrays $A$-sequence $Z$-sequence $(c)$-Bell polynomials $(c)$-hitting-time subgroup |
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