Two general families of integer-valued polynomials associated with finite trigonometric sums

A dozen families of integer-valued polynomials arising in finite summation of various trigonometric sums are known and all of them were deduced through numerical analysis methods. Here, using simple arguments commonly applied in work with polynomial sequences, we examined such expressions in full detail as well as in a systematic and unified manner. Two new very general integer-valued polynomial families (along with six other families derived from them, also integer-valued, including three previously studied) were obtained and they are related to each other by a binomial transform of sequences and associated with certain cosecant and cotangent sums. (C) 2020 Elsevier Inc. All rights reserved.