Wolfdieter Lang

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Sequences of generalized Stirling numbers of both kinds are introduced. These sequences of triangles (i.e. infinite-dimensional lower triangular matrices) of numbers will be denoted by S2(k;n,m) and S1(k;n,m) with k ∈ Z. The original Stirling number triangles of the second and first kind arise when k = 1. S2(2;n,m) is identical with the unsigned S1(2;n,m)(More)
with α(x) = f(x)/f0(x), β(x) = f1(x)/f0(x), and γ(x) = f2(x)/f0(x). Let G(x) generate the number sequence {Gn}0 , i.e. G(x) = ∑∞ n=0Gnx . Because G(x) is the generating function for the convolution of the sequence {Gn}0 with itself, i.e. of G (1) n := ∑n k=0GkGn−k, one can use eq. 2 in order to express the convolution numbers G n in terms of {Gk} 0 and the(More)