Related papers: Tables of convolution integrals
In this expository article, we provide a self-contained overview of the notion of convolution embedded in different theories: from the classical Fourier theory to the theory of algebraic signal processing. We discuss their relations and…
An analytical-numeric calculation method of extremely complicated integrals is presented. These integrals appear often in magnet soliton theory. The appropriate analytical continuation and a corresponding integration contour allow to reduce…
The concept of permutograph is introduced and properties of integral functions on permutographs are established. The central result characterizes the class of integral functions that are representable as lattice polynomials. This result is…
We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting…
In these lectures I will give an introduction to Feynman integrals. In the first part of the course I review the basics of the perturbative expansion in quantum field theories. In the second part of the course I will discuss more advanced…
We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage…
Two approximations of the integral of a class of sinusoidal composite functions, for which an explicit form does not exist, are derived. Numerical experiments show that the proposed approximations yield an error that does not depend on the…
A characterization of multiplicative (and additive) arithmetical functions is given. Using this characterization, we show that the group of multiplicative arithmetical functions is isomorphic to the group of additive arithmetical functions.
I present a highly efficient method for evolving parton distributions in perturbative QCD. The method allows evolving the parton distribution functions according to any of the commonly-used truncations of the evolution equations (which…
In this paper we present a special formula for transforming integrals to series. The resulting series involves binomial transforms with the Taylor coefficients of the integrand. Five applications are provided for evaluating challenging…
This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.
The functions on a lattice generated by the integer degrees of $q^2$ are considered, 0<q<1. The $q^2$-translation operator is defined. The multiplicators and the $q^2$-convolutors are defined in the functional spaces which are dual with…
Some properties of integral averages of functions on intervals and their asymptotic behavior are investigated. The results are aimed at applications to entire and subharmonic functions.
We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable.
A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…
We present a method derived from Laplace transform theory that enables the evaluation of fractional integrals. This method is adapted and extended in a variety of ways to demonstrate its utility in deriving alternative representations for…
A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized…
Convolution sums are introduced and special instances of the cyclic convolution on finite sets is examined in more detail. The distributions that emerge are multidimensional generalizations of the Catalan and Narayana numbers. This work…
``Quasi-elliptic'' functions can be given a ring structure in two different ways, using either ordinary multiplication, or convolution. The map between the corresponding standard bases is calculated. A related structure has appeared…
Discrete analogs of the Lebedev transforms with the product of the modified Bessel functions are introduced and investigated. Several expansions of suitable functions and sequences in terms of the series and integrals, involving the…