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Cheon, Gi-Sang; Forgács, Tamás; Kim, Hana; Tran, Khang
Journal of mathematical analysis and applications, 10/2022, Volume: 514, Issue: 1Journal Article
We present combinatorial and analytical results concerning a Sheffer sequence with a generating function of the form G(x,z)=Q(z)xQ(−z)1−x, where Q is a quadratic polynomial with real zeros. By using the properties of Riordan matrices we address combinatorial properties and interpretations of our Sheffer sequence of polynomials and their coefficients. We also show that apart from two exceptional zeros, the zeros of polynomials with large enough degree in such a Sheffer sequence lie on the line x=1/2+it.
