Related papers: Telescoping method, derivative operators and harmo…
Definite integrals with parameters of holonomic functions satisfy holonomic systems of linear partial differential equations. When we restrict parameters to a one dimensional curve, the system becomes a linear ordinary differential equation…
In this paper, we are concerned with the construction and analysis of a new class of methods obtained as double jump compositions with complex coefficients and projection on the real axis. It is shown in particular that the new integrators…
Every year, hundreds of images from telescopes on the ground and in space are released to the public, making their way into popular culture through everything from computer screens to postage stamps. These images span the entire…
In this paper, we study the theory of the harmonic and the hyperharmonic Fibonacci numbers. Also, we get some combinatoric identities like as harmonic and hyperharmonic numbers and we obtain some useful formulas for $\mathbb{F}_{n}$, which…
We give a new expression of the multiple harmonic sum, which serves as a refinement of the iterated integral expression of the multiple zeta value, and prove it using the so-called connected sum method. Based on this fact, by taking two…
Thermoacoustic tomography is a term for the inverse problem of determining of one of initial conditions of a hyperbolic equation from boundary measurements. In the past publications both stability estimates and convergent numerical methods…
Numerical experiments with smooth surface extension and image inpainting using harmonic and biharmonic functions are carried out. The boundary data used for constructing biharmonic functions are the values of the Laplacian and normal…
Some properties and relations satisfied by the polynomial solutions of the bispectral problem are studied. Given a differential operator, under certain restrictions its polynomial eigenfunctions are explicitly obtained, as well as the…
We present a criterion for the existence of telescopers for mixed hypergeometric terms, which is based on multiplicative and additive decompositions. The criterion enables us to determine the termination of Zeilberger's algorithms for mixed…
In this work we deal with a symbolic approach to the general quadratic polynomial decomposition. By means of a symbolic implementation, we investigate some properties of the components sequences like orthogonality and symmetry. We present…
We realize that geometric polynomials and p-Bernoulli polynomials and numbers are closely related with an integral representation. Therefore, using geometric polynomials, we extend some properties of Bernoulli polynomials and numbers such…
It is proved that harmonic functions are characterized by harmonicity of their spherical means, for which purpose the iterated spherical means are used. The similar characterization of solutions to the modified Helmholtz equation…
The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity…
We apply symmetry and invariance methods to analyse systems of difference equations. Non trivial symmetries are derived and their exact solutions obtained.
We discuss reflections identities of harmonic sums up to weight three. The need for this kind of identities emerges in analysis of the general structure of eigenvalue of the BFKL equation. The reflection identities decompose a product of…
Before we proposed an algebraic technics for the Hamiltonian approach to the evolution systems of partial differential equations, including systems with constraints. Here we further develop this approach and present the defining system of…
The methods of integral operators on the cohomology of Hilbert schemes of points on surfaces are developed. They are used to establish integral bases for the cohomology groups of Hilbert schemes of points on a class of surfaces (and…
We give a proof of two identities involving binomial sums at infinity conjectured by Z-W Sun. In order to prove these identities, we use a recently presented method i.e. we view the series as specializations of generating series and derive…
We extend to higher order a recently published method for calculating the deflection angle of light in a general static and spherically symmetric metric. Since the method is convergent we obtain very accurate analytical expressions that we…
We give algorithms to compute decompositions of a given polynomial, or more generally mixed tensor, as sum of rank one tensors, and to establish whether such a decomposition is unique. In particular, we present methods to compute the…