Sequences and Series/Dirichlet‒Hurwitz series

Dirichlet‒Hurwitz series Let be a function, and let . The Dirichlet‒Hurwitz series associated to and is the function of given by the series . abscissa of absolute convergence of Dirichlet‒Hurwitz series Let be a function, and let . Suppose that there exists a number such that converges whenever and diverges whenever . Then is called the abscissa of absolute convergence of the Dirichlet‒Hurwitz series associated to and . existence of abscissa of absolute convergence of Dirichlet‒Hurwitz series Let be a function, and let . Suppose that