doiSerbia

Finite sums involving trigonometric functions and special polynomials: Analysis of generating functions and p-adic integrals

Kilar Neslihan (Department of Computer Technologies, Bor Vocational School, Niğde Ömer Halisdemir University, Niğde, Turkey), neslihankilar@ohu.edu.tr; neslihankilar@gmail.com
Bayad Abdelmejid (Laboratoire de Mathématiques et Modélisation d’Évry (LAMME), UniversitÉ Paris-Saclay, CNRS (UMR), Bâtiment I.B.G.B.I., CEDEX, Evry, France), abdelmejid.bayad@univ-evry.fr
Simsek Yilmaz (Department of Mathematics, Faculty of Science, University of Akdeniz, Antalya, Turkey), ysimsek@akdeniz.edu.tr; ysimsek@gmail.com

By using trigonometric and generating functions, some formulas and relations involving sums of powers of consecutive positive integers and certain combinatorial sums are derived. By applying the derivative operator to some certain families of special functions and finite sums involving trigonometric functions, many novel relations related to the special numbers and polynomials are obtained. Moreover, by applying p-adic integrals to these finite sums, some p-adic integral representations of trigonometric functions are found.

Keywords: Bernoulli and Euler numbers and polynomials, Stirling numbers, Combinatorial numbers and sums, Special functions, p-adic integrals