Characterization of (c)-Riordan arrays, Gegenbauer-Humbert-type Polynomial Sequences, and (c)-Bell Polynomials

Publication Date



The Journal of Mathematical Research with Applications is published by Dalian University of Technology and China Society for Industrial and Applied Mathematics,


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.