The Properties of Lower Triangular Matrix Associated with Polynomial of Binomial Type
Tianming Wang · Journal of Mathematical Research and Exposition · 2005
The properties of the lower triangular functional matrix Ln[x] associated with a polynomial of binomial type are discussed in this paper, in which the entry-(i,j) of Ln[x] is equal to lij =(?)i-j(x)l(i,j)if i≥j and equal to 0 otherwise, with l(i, k)l(k,j) = l(i,j)(k-j i-j) and for integers n,k,i,j and real numbers x,y. Pascal matrix and its generalizations are special cases of Ln[x]. More general results and some combinatorial identities are derived.