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Given a Sheffer sequence of polynomials, we introduce the notion of anassociated sequence called the cognate sequence. We study the relationshipbetween the zeros of this pair of associated sequences and show that in case ofan Appell sequence, as well as a more general family of Sheffer sequences, thezeros of the members of each sequence (for large n) are either real, or lie ona line $\Re (z)=c$. In addition to finding the zero locus, we also find thelimiting probability distribution function of such sequences.

On the zeros of certain Sheffer sequences and their cognate sequences