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This article presents two methods, in parallel, of solving more complex integrals, among which is the Poisson's integral, in order to emphasize the obvious advantages of a new method of integration, which uses the supermathematics circular…
This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…
We construct a meromorphic function on the eigencurve that interpolates a square root of the ratio of the central values of two quadratic twists of the $L$-function at classical points.
In this article, a class of analytic functions is investigated and their some properties are established. Several recurrence relations and various classes of bilinear and bilateral generating functions for these analytic functions are also…
Considering the kernel of an integral operator intertwining two realizations of the group of motions of the pseudo-Euclidian space, we derive two formulas for series containing Whittaker's functions or Weber's parabolic cylinder functions.…
Partial Fourier transforms are used to find explicit formulas for two remarkable fundamental solutions for a generalized Tricomi operator. These fundamental solutions reflect clearly the mixed type of the operator. In order to prove these…
Special values of the Lommel functions allow the calculation of Fresnel like integrals. These closed form expressions along with their asymptotic values are reported.
A systematic study of the representation theory of double affine Hecke algebras and related harmonic analysis is started in this paper. Continuing the previous papers we use the technique of intertwining operators to create Macdonald…
The central idea of this article is to present a systematic approach to construct some recurrence relations for the solutions of the second-order linear difference equation of hypergeometric-type defined on the quadratic-type lattices. We…
Usually such area of mathematics as differential equations acts as a consumer of results given by functional analysis. This article will give an example of the reverse interaction of these two fields of knowledge. Namely, the derivation and…
We introduce an analog of part of the Langlands-Shahidi method to the p-adic setting, constructing reciprocals of certain p-adic L-functions using the nonconstant terms of the Fourier expansions of Eisenstein series. We carry out the method…
We develop a technique that solders the dual aspects of some symmetry. Using this technique it is possible to combine two theories with such symmetries to yield a new effective theory. Some applications in two and three dimensional…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their…
Analytic expressions for the Fourier transforms of the Chebyshev and Legendre polynomials are derived, and the latter is used to find a new representation for the half-order Bessel functions. The numerical implementation of the so-called…
This work proves pointwise convergence of the truncated Fourier double integral of non-Lebesgue integrable bounded variation functions. This leads to the Dirichlet-Jordan theorem proof for non-Lebesgue integrable functions, which has not…
In this work, we study vector-valued functional equations with multiple recursive terms that arise naturally when we are dealing with vector-valued multiplicative Lindley-type recursions. We provide a detailed framework for the solution of…
Multiple-integral representations of the (skew-)Macdonald symmetric functions are obtained. Some bosonization schemes for the integral representations are also constructed.
Some practical applications of algebraic renormalization are discussed. In particular we consider the two-loop QCD corrections to the three-gauge-boson vertices involving photons, Z and W bosons. For this purpose also the corresponding…
The aim of the present study is to establish some properties for q-Bessel matrix polynomials such as several q-differential matrix equation, q-differential matrix relations and q-recurrence matrix relations, and integral representation,…