On the zeros of certain polynomials and entire functions

Abstract

Entire functions whose coefficients are polynomials having real and negative roots are built from Touchard polynomials. The particular set of polynomials (Formula Presented) is shown to have purely complex roots, where we show a connection of these polynomials with certain approximations of the Riemann’s zeta function. Also a certain class of Fourier transforms is shown to have only real roots.