相关论文: A radius of absolute convergence for power series …

An effective radius of convergence is defined and computed for any truncated Taylor series. Applications to well known series are performed and is shown that a range of good coincidence for actual and approximative plot can always be found.…

This paper describes an algorithm for determining radii of convergence of power expansions for algebraic functions and the testing done to check it. Since the current methods for computing these series are iterative, standard methods for…

In this paper we prove an $n$th root test for series as well as a Cauchy-Hadamard type formula and Abel's' theorem for power series on universally complete Archimedean complex vector lattices. These results are aimed at developing an…

The purpose of this article is to provide an exposition of domains of convergence of power series of several complex variables without recourse to relatively advanced notions of convexity.

Given a power series in finitely many variables that is algebraic over the corresponding polynomial ring over a subfield of the reals, we show that its convergence domain is semialgebraic over the real closure of the subfield. This gives in…

A convergent power series solution is obtained for the SIR model, using an asymptotically motivated gauge function. For certain choices of model parameter values, the series converges over the full physical domain (i.e., for all positive…

An exact representation of the Baker-Campbell-Hausdorff formula as a power series in just one of the two variables is constructed. Closed form coefficients of this series are found in terms of hyperbolic functions, which contain all of the…

By a theorem of Strassmann, a non-zero convergent power series in one variable over a complete non-Archimedean field has finitely many zeros, with an explicit bound on their number. We generalize this result to convergent power series in…

We present a systematic study on the linear convergence rates of the powers of (real or complex) matrices. We derive a characterization when the optimal convergence rate is attained. This characterization is given in terms of…

In this work it is presented an exact power series formula for the Kallen-Sabry vacuum polarization potential.

We study the existence of formal power series solutions to q-algebraic equations. When a solution exists, we give a sufficient condition on the equation for this solution to have a positive radius of convergence. We emphasize on the case…

In this paper we have discussed convergence of power series both in p-adic norm as well as real norm. We have investigated rational summability of power series with respect to both p-adic norm and real norm under certain conditions. Then we…

We construct an explicit filtration of the ring of algebraic power series by finite dimensional constructible sets, measuring the complexity of these series. As an application, we give a bound on the dimension of the set of algebraic power…

In this article we derive an approximation inequality for continued radicals, generalizing an inequality of Herschfeld for continued square roots to arbitrary radicals, which is useful in exploring convergence issues and obtaining…

Power series are introduced that are simultaneously convergent for all real and p-adic numbers. Our expansions are in some aspects similar to those of exponential, trigonometric, and hyperbolic functions. Starting from these series and…

The Bohr radius for power series of holomorphic functions mapping a multidimensional Reinhardt domain into the convex domain in the complex plane is independent of this convex domain.

High-order derivatives of analytic functions are expressible as Cauchy integrals over circular contours, which can very effectively be approximated, e.g., by trapezoidal sums. Whereas analytically each radius r up to the radius of…

This note gives a few rapidly convergent series representations of the sums of divisors functions. These series have various applications such as exact evaluations of some power series, computing estimates and proving the existence results…

We consider a formal power series in one variable whose coefficients are holomorphic functions in a given multidimensional complex domain. Assume the following two conditions on the series. (C1) The restriction of the series at each point…

The study of the convergence of power series expansions of energy eigenvalues for anharmonic oscillators in quantum mechanics differs from general understanding, in the case of quasi-exactly solvable potentials. They provide examples of…