A General Class of the Three-Variable Unified Apostol-Type q-Polynomials and Multiple Power q-Sums - Srivastava, Hari M.; Khan, Subuhi; Araci, Serkan; Acikgoz, Mehmet; Riyasat, Mumtaz; Aracı, Serkan (Springer International Publishing, 2019)
The main purpose of this article is to introduce a general class of the three-variable unified Apostol-type q-polynomials and to investigate their properties and characteristics. In particular, the generating function, series expression, and several explicit and recurrence relations for these polynomials are established. The three-variable general Apostol–Bernoulli, Apostol–Euler, and Apostol–Genocchi q-polynomials are studied as special members of this class and the corresponding results for these q-polynomials are also obtained. Some symmetry identities involving multiple power q-sums are established. The particular cases of these identities are also deduced. This article presents the first attempt in the direction of establishing symmetry identities for the generalized class of q-polynomials. © 2019, Iranian Mathematical Society.
Keywords: General q-polynomials; Symmetry identities; Three-variable unified general Apostol-type q-polynomials; Unified Apostol-type q-polynomials