Related papers: Holomorphic extensions associated with series expa…
In this article we prove that if the coefficients of a Fourier-Legendre expansion satisfy a suitable Hausdorff-type condition, then the series converges to a function which admits a holomorphic extension to a cut-plane. Furthermore, we…
Based on the full similarity in algebraic properties and differentiation rules between quaternionic (H-) holomorphic and complex (C-) holomorphic functions, we assume that there exists one holistic notion of a holomorphic function that has…
Physically relevant field-theoretic quantities are usually derived from perturbation techniques. These quantities are solved in the form of an asymptotic series in powers of small perturbation parameters related to the physical system, and…
This paper studies the equivalence between generalized holomorphic functions (GHF) and complex analytic functions in the framework of Robinson-Colombeau generalized numbers. In every non-Archimedean ring, the use of ordinary series is…
Let $B_{R}$ be the ball in the euclidean space $\mathbb{R}^{n}$ with center 0 and radius $R$ and let $f$ be a complex-valued, infinitely differentiable function on $B_{R}.$ We show that the Laplace-Fourier series of $f$ has a holomorphic…
The main objective of this article is a constructive generalization of the holomorphic power and Laurent series expansions in C to dimension 3 using the framework of hypercomplex function theory. For this reason, deals the first part of…
Let G be a connected, real, semisimple Lie group contained in its complexification G_C, and let K be a maximal compact subgroup of G. We construct a K_C-G double coset domain in G_C, and we show that the action of G on the K-finite vectors…
We study the analog of power series expansions on the Sierpinski gasket, for analysis based on the Kigami Laplacian. The analog of polynomials are multiharmonic functions, which have previously been studied in connection with Taylor…
We consider the problem of continuability into a sectorial domain for multiple power series and prove the multivariate analog of the Le Roy-Lindel\"of theorem, i.e. establish a connection between the growth of the holomorphic function…
Previously, we introduced a method for systematically correcting a quasiparticle green's function via a power series expansion. Here we present an ODE based formalisms of power series correction that goes beyond the cumulant approximation…
This introductory paper studies a class of real analytic functions on the upper half plane satisfying a certain modular transformation property. They are not eigenfunctions of the Laplacian and are quite distinct from Maass forms. These…
Let $w$ be an unbounded radial weight on the complex plane. We study the following approximation problem: find a proper holomorphic map $f: \mathbb{C}\to\mathbb{C}^n$ such that $|f|$ is equivalent to $w$. We give several characterizations…
Let x be a CM point on a modular or Shimura curve and p a prime of good reduction, split in the CM field K. We define an expansion of an holomorphic modular form f in the p-adic neighborhood of x and show that the expansion coefficients…
Expressions for the thermodynamic and transport properties of plasmas are derived from quantum statistics in the form of equilibrium correlation functions. These can be evaluated using analytical methods or numerical approaches such as…
We derive an integral-free thermodynamic perturbation series expansion for quantum partition functions which enables an analytical term-by-term calculation of the series. The expansion is carried out around the partition function of the…
This text is about the mathematical use of certain divergent power series. The first part is an introduction to 1-summability. The definitions rely on the formal Borel transform and the Laplace transform along an arbitrary direction of the…
We present a modified version of the Arakelyan's result: a relationship between holomorphic extension of a holomorphic function on the unit disc onto the domain $\mathbb C\setminus[1,\infty)$ and its Taylor coefficients' interpolation.
By exploiting the analyticity and boundary value properties of the thermal Green functions that result from the KMS condition in both time and energy complex variables, we treat the general (non-perturbative) problem of recovering the…
The algebraic properties of formal power series, whose coefficients show factorial growth and admit a certain well-behaved asymptotic expansion, are discussed. It is shown that these series form a subring of $\mathbb{R}[[x]]$. This subring…
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…