Generalized Gregory's series

John Gregory and the invention of professional medical ethics and the profession of medicine

We do not expect sympathy from a good accountant, or a good lawyer. An unsympathetic accountant or lawyer can be good, we might even take the lack of sympathy to be a mark of professionalism; however, there is something profoundly wrong, even unprofessional, about unsympathetic physicians. Good doctors ought to have a caring heart. We inherit this expectation from the Scottish Enlightenment. Un...

Uniserial modules of generalized power series

Let R be a ring, M a right R-module and (S,≤) a strictly ordered monoid. In this paper we will show that if (S,≤) is a strictly ordered monoid satisfying the condition that 0 ≤ s for all s ∈ S, then the module [[MS,≤]] of generalized power series is a uniserial right [[RS,≤]] ]]-module if and only if M is a simple right R-module and S is a chain monoid.

Generalized Ritt type and generalized Ritt weak type connected growth properties of entire functions represented by vector valued Dirichlet series

In this paper, we introduce the idea of generalized Ritt type and generalised Ritt weak type of entire functions represented by a vector valued Dirichlet series. Hence, we study some growth properties of two entire functions represented by a vector valued Dirichlet series on the basis of generalized Ritt type and generalised Ritt weak type.

On Some Results in the Light of Generalized Relative Ritt Order of Entire Functions Represented by Vector Valued Dirichlet Series

In this paper, we study some growth properties of entire functions represented by a vector valued Dirichlet series on the basis of generalized relative Ritt order and generalized relative Ritt lower order.

A Numerical Integration Method by Using Generalized Series of Functions