Related papers: Global reconstruction of analytic functions from l…
We introduce a new representation for the rescaled Appell polynomials and use it to obtain asymptotic expansions to arbitrary order. This representation consists of a finite sum and an integral over a universal contour (i.e. independent of…
Recently, we have established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of analytical function to obtain a few new criteria equivalent to the Riemann hypothesis. Here, the same theorem is…
Summation formulas, such as the Euler-Maclaurin expansion or Gregory's quadrature, have found many applications in mathematics, ranging from accelerating series, to evaluating fractional sums and analyzing asymptotics, among others. We show…
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 considers functional series whose terms are higher-order derivatives of Chebyshev polynomials of the second kind, where the degree of the polynomial is related to the order of the derivative. Analytic summation is used to…
I present a novel mathematical technique for dealing with the infinities arising from divergent sums and integrals. It assigns them fine-grained infinite values from the set of hyperreal numbers in a manner that refines the standard…
We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool…
Localization is a topological technique that allows us to make global equivariant computations in terms of local data at the fixed points. For example, we may compute a global integral by summing integrals at each of the fixed points. Or,…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
We state and prove a general summation identity. The identity is then applied to derive various summation formulas involving the generalized harmonic numbers and related quantities. Interesting results, mostly new, are obtained for both…
We propose a new method for obtaining complete asymptotic expansions in a systematic manner, which is suitable for counting sequences of various graph families in dense regime. The core idea is to encode the two-dimensional array of…
We introduce a new formulation of the so-called topological recursion, that is defined globally on a compact Riemann surface. We prove that it is equivalent to the generalized recursion for spectral curves with arbitrary ramification. Using…
A general method for analytic inversion of geometric integral transforms is proposed
We consider the problem of analyzing the heterogeneity of clustering distributions for multiple groups of observed data, each of which is indexed by a covariate value, and inferring global clusters arising from observations aggregated over…
Self-adjoint Dirac systems and subclasses of canonical systems, which generalize Dirac systems are studied. Explicit and global solutions of direct and inverse problems are obtained. A local Borg-Marchenko-type theorem, integral…
The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of…
Expansions of physical functions are controlled by their singularities, which have special structure because they themselves are physical, corresponding to instantons, caustics or saddle configurations. Resurgent asymptotics formalizes this…
Differintegral methods, currently exploited in calculus, provide a fairly unexhausted source of tools to be applied to a wide class of problems involving the theory of special functions and not only. The use of integral transforms of Borel…
The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…
This work introduces a new functional series for expanding an analytic function in terms of an arbitrary analytic function. It is generally applicable and straightforward to use. It is also suitable for approximating the behavior of a…