Related papers: On a multiple harmonic power series
In this paper, we present formula solutions of a family of difference equations of higher order. We discuss the periodic nature of the solutions and we investigate the stability character of the equilibrium points. We utilize Lie symmetry…
In the revised version of the paper, we correct misprints and add some new statements.
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…
A bi-Hamiltonian formulation is proposed for triangular systems resulted by perturbations around solutions, from which infinitely many symmetries and conserved functionals of triangular systems can be explicitly constructed, provided that…
In this paper, we present several explicit formulas of the sums and hyper-sums of the powers of the first (n+1)-terms of a general arithmetic sequence in terms of Stirling numbers and generalized Bernoulli polynomials.
In a previous work (arXiv:2505.05574), a summation formula for harmonic Maass forms of polynomial growth was established. In this note, we use the theory of $L$-series of harmonic Maass forms to state and prove a summation formula for such…
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.
We present here a large collection of harmonic and quadratic harmonic sums, that can be useful in applied questions, e.g., probabilistic ones. We find closed-form formulae, that we were not able to locate in the literature.
The goal of the paper is multi-fold. First, an explicit formula is derived to compute the non-commutative generating series of a closed-loop system when a (multi-input, multi-output) plant, given in Chen--Fliess series description is in…
Explicit evaluations of the Tornheim-like double series in the form \[ \sum_{n,m=1}^\infty \frac{H_{n+m+s}}{nm\left( n+m+s \right)},\ s\in \mathbb{N\cup } \left\{ 0 \right\} \] and their extensions are given. Furthermore, series of the type…
Some finite series of harmonic numbers involving certain reciprocals are evaluated. Products of such reciprocals are expanded in a sum of the individual reciprocals, leading to a computer program. A list of examples is provided.
A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…
In this short note we recall the definition of intrinsically harmonic forms, some known results and some open problems.
Recent theoretical progress in calculations of the spectrum and decays of charmonium is reviewed. Traditionally, our understanding of charmonium was based on potential models. This is now being replaced by first principles.
In this paper, we obtain some new upper bounds for differantiable mappings whose q-th powers are geometrically convex and monotonically decreasing by using the H\"older inequality, Power mean inequality and properties of modulus.
We supplement the result of the first part of the work with estimates of the integrals of the difference of subharmonic functions in measure with some deterioration of the absolute constants, but these estimates have the form of a…
Stability of power networks is an increasingly important topic because of the high penetration of renewable distributed generation units. This requires the development of advanced (typically model-based) techniques for the analysis and…
Exterior power operations on the higher $K$-groups of a quasi-compact scheme have recently been constructed by Taelman and the authors by purely algebraic means. In this paper, we prove two formulae that help to compute these operations.…
We show the existence of periodic solutions for continuous symmetric perturbations of certain planar power law problems.
We introduce several properties of forcing notions which imply that their lambda-support iterations are lambda-proper. Our methods and techniques refine those studied in math.LO/9906024, math.LO/0210205, math.LO/0508272 and math.LO/0605067,…