In this paper, we establish Möbius inversion formulae for the Fourier expansions of the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. As an application, by specializing our ...
Algebraic structures, ranging from groups and rings to modules and fields, constitute the foundation of modern mathematics. Among these, Hopf algebras have emerged as pivotal constructions that ...