Another two families of integer-valued polynomials associated with finite trigonometric sums

Abstract

As a sequel to our recent paper, its general approach was here extended to finite alternating trigonometric sums giving rise to polynomials which were systematically examined in full detail as well as in a unified manner using simple arguments. Two new general families of integer-valued polynomials (along with four other families derived from them, also integer-valued, including two already known) were deduced. Also, these polynomials enable closed-form summation of a great deal of general families of finite sums.