Generalized Riordan arrays and zero generalized Pascal matrices [article]

E. Burlachenko
2016 arXiv   pre-print
Generalized Pascal matrix whose elements are generalized binomial coefficients is included in the group of generalized Riordan arrays. There is a special set of generalized Riordan arrays defined by parameter q. If q=0, they are ordinary Riordan arrays, if q=1, they are exponential Riordan arrays. In other cases, except q=-1, they are arrays associated with the q-binomial coefficients as well as the exponential Riordan arrays are associated with the ordinary binomial coefficients. Case q=-1
more » ... not fit into the concept of generalized Riordan arrays, but it is necessary to expand for it. Introduced a special class of matrices, each of which is a limiting case of a certain set of generalized Pascal matrices. It is shown that every such matrix included in the matrix group similar to the generalized Riordan group.
arXiv:1612.07657v1 fatcat:s4uxp36cyrgkzbwg5xmenor7lq