Related papers: DoFun 3.0: Functional equations in Mathematica
We continue the study of the correlation functions for the point stochastic processes introduced in Part I (G.Olshanski, math.RT/9804086). We find an integral representation of all the correlation functions and their explicit expression in…
We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the…
This article describes the implementation in the software package NumGfun of classical algorithms that operate on solutions of linear differential equations or recurrence relations with polynomial coefficients, including what seems to be…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
We propose a functional calculus which allows one to apply functions to the matrix anti-commutator/commutator operator. The calculus is introduced in a straightforward manner if the operators act on symmetric matrices, and it leads to a…
The standard engineering approach to modelling of complex systems is highly compositional. In order to be able to understand (or to control) the behavior of a complex dynamical systems, it is often desirable, if not necessary, to view this…
The Functional Machine Calculus (Heijltjes 2022) is an extension of the lambda-calculus that preserves confluent reduction and typed termination, while enabling both call-by-name and call-by-value reduction behaviour and encoding the…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
We present an approach to obtain formally verified implementations of classical Computational Logic algorithms. We choose the Why3 platform because it allows to implement functions in a style very close to the mathematical definitions, as…
We present a new version of TaylUR, a Fortran 95 module to automatically compute the numerical values of a complex-valued function's derivatives with respect to several variables up to an arbitrary order in each variable, but excluding…
Two-dimensional sl(n) quantum Toda field theory on a sphere is considered. This theory provides an important example of conformal field theory with higher spin symmetry. We derive the three-point correlation functions of the exponential…
Conical functions appear in a large number of applications in physics and engineering. In this paper we describe an extension of our module CONICAL for the computation of conical functions. Specifically, the module includes now a routine…
Incremental computation has recently been studied using the concepts of change structures and derivatives of programs, where the derivative of a function allows updating the output of the function based on a change to its input. We…
This article introduces the Mathematica package \emph{HEPMath} which provides a number of utilities and algorithms for High Energy Physics computations in Mathematica. Its functionality is similar to packages like FormCalc or FeynCalc, but…
We give yet another proof for Fa\`{a} di Bruno's formula for higher derivatives of composite functions. Our proof technique relies on reinterpreting the composition of two power series as the generating function for weighted integer…
The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional equation), quantum field theory (Schwinger-Dyson equations)…
Functional equations (FE) arise quite naturally in the analysis of stochastic systems of different kinds : queueing and telecommunication networks, random walks, enumeration of planar lattice walks, etc. Frequently, the object is to…
We present version 4.0 of the symbolic manipulation system FORM. The most important new features are manipulation of rational polynomials and the factorization of expressions. Many other new functions and commands are also added; some of…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
In this paper we develop a technique of computation of correlation functions in theories with action being cubic or higher degree form in terms of discriminants of corresponding tensors. These are analogues of formula $\int \exp…