Related papers: Olsson.wl : a Mathematica package for the computat…

Series involving hypergeometric functions are used to derive, extend and evaluate integrals involving the product of two Bessel functions of the first kind $J_{u}(a z)$ $J_{v}(b z)$ with order $u,v$, studied by Landau et al. The method used…

Two unitary integral transforms with a very-well poised $_7F_6$-function as a kernel are given. For both integral transforms the inverse is the same as the original transform after an involution on the parameters. The $_7F_6$-function…

The aim of this paper is to give an explicit formula for the nonsymmetric Heckman-Opdam's hypergeometric function of type $A_2$. This is obtained by differentiating the corresponding symmetric hypergeometric function.

This survey article (which will appear as a chapter in the book ``Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions'', Springer-Verlag) provides a small collection of basic material on multiple…

Integral representations of hypergeometric functions proved to be a very useful tool for studying their properties. The purpose of this paper is twofold. First, we extend the known representations to arbitrary values of the parameters and…

The generalized hypergeometric function $_qF_p$ is a power series in which the ratio of successive terms is a rational function of the summation index. The Gaussian hypergeometric functions $_2F_1$ and $_3F_2$ are most common special cases…

We derive some Euler type double integral representations for hypergeometric functions in two variables. In the first part of this paper we deal with Horn's $H_2$ function, in the second part with Olsson's $F_P$ function. Our double…

This article gives a classification scheme of algebraic transformations of Gauss hypergeometric functions, or pull-back transformations between hypergeometric differential equations. The classification recovers the classical transformations…

This exposition presents nimblewomble, a software package to perform wombling, or boundary analysis, using the nimble Bayesian hierarchical modeling language in the R statistical computing environment. Wombling is used widely to track…

A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the…

This paper describes the R package mvLSW. The package contains a suite of tools for the analysis of multivariate locally stationary wavelet (LSW) time series. Key elements include: (i) the simulation of multivariate LSW time series for a…

It is demonstrated that the well-regularized hypergeometric functions can be evaluated directly and numerically. The package NumExp is presented for expanding hypergeometric functions and/or other transcendental functions in a small…

We describe TensoriaCalc, a tensor calculus package written to be smoothly consistent with the Wolfram Language, so as to ensure ease of usage. It allows multiple metrics to be defined in a given session; and, once a metric is computed,…

This note introduces the $\texttt{LikelihoodGeometry}$ package for the computer algebra system $\textit{Macaulay2}$. This package gives tools to construct the likelihood correspondence of a discrete algebraic statistical model, a variety…

The two most commonly used hypergeometric functions are the confluent hypergeometric function and the Gauss hypergeometric function. We review the available techniques for accurate, fast, and reliable computation of these two hypergeometric…

The construction of a multiresolution analysis starts with specification of a scale function. The Fourier transform of this function is defined by an infinite product. The convergence of this product is usually discussed in the context of…

We give an introduction to the Mathematica packages "MasterPVA" and "MasterPVAmulti used to compute lambda-brackets in Poisson vertex algebras, which play an important role in the theory of infinite-dimensional Hamiltonian systems. As an…

In this paper we present a short overview of the new Wolfram Mathematica package intended for elementary "in-basis" tensor and differential-geometric calculations. In contrast to alternatives our package is designed to be easy-to-use,…

This paper shows that certain $\,_{3}F_{4}$ hypergeometric functions can be expanded in sums of pair products of $\,_{1}F_{2}$ functions. In special cases, the $\,_{3}F_{4}$ hypergeometric functions reduce to $\,_{2}F_{3}$ functions.…

This paper introduces two novel approaches for Online Multi-Task Learning (MTL) Regression Problems. We employ a high performance graph-based MTL formulation and develop two alternative recursive versions based on the Weighted Recursive…