Related papers: HYPERgeometric functions DIfferential REduction: M…

Universal geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. This paper treats the fundamentals of the multivector differential…

The exact (closed form) solutions of the equations of motion in the theory of general relativity that describe motion of test particle and photon in Kerr and Kerr-(anti) de Sitter spacetimes all involve the multivariable hypergeometric…

Let $E_C$ be the hypergeometric system of differential equations satisfied by Lauricella's hypergeometric series $F_C$ of $m$ variables. We show that the monodromy representation of $E_C$ is irreducible under our assumption consisting of…

Hyper-heuristics are a novel tool. They deal with complex optimization problems where standalone solvers exhibit varied performance. Among such a tool reside selection hyper-heuristics. By combining the strengths of each solver, this kind…

Calculus of Variation combined with Differential Geometry as tools of modelling and solving problems in image processing and computer vision were introduced in the late 80's and the 90s of the 20th century. The beginning of an extensive…

Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these…

We have developed a Mathematica package capable of performing gamma-matrix algebra in arbitrary (integer) dimensions. As an application we can compute Fierz transformations.

In this paper, we investigate the relationships among hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions through some families of `hypergeometric' algebraic varieties that are higher dimensional…

Discrete analogs of the classical Fourier-Jacobi transform are introduced and investigated. It involves series and integrals with respect to parameters of the Gauss hypergeometric function ${}_2F_1(a+in/2,a-in/2;\ c; -x^2 ), \ x >0, n \in…

Finite hypergeometric functions are complex valued functions on finite fields which are the analogue of the classical analytic hypergeometric functions. From the work of N.M.Katz it follows that their values are traces of Frobenius on…

Many problems in Physics and Chemistry are formulated as the minimization of a functional. Therefore, methods for solving these problems typically require differentiating maps whose input and/or output are functions -- commonly referred to…

We present two algorithms for computing hypergeometric solutions of second order linear differential operators with rational function coefficients. Our first algorithm searches for solutions of the form \[ \exp(\int r \,…

We obtain new inequalities for certain hypergeometric functions. Using these inequalities, we deduce estimates for the hyperbolic metric and the induced distance function on a certain canonical hyperbolic plane domain.

We present both the Lagrangian and Hamiltonian procedures for treating higher-order equations of motion for mechanical models by adopting the Riemann-Liouville Fractional integral to describe their action. We point out and discuss its…

In this paper, we build on the work of [T. Hughes, G. Sangalli, VARIATIONAL MULTISCALE ANALYSIS: THE FINE-SCALE GREENS' FUNCTION, PROJECTION, OPTIMIZATION, LOCALIZATION, AND STABILIZED METHODS, SIAM Journal of Numerical Analysis, 45(2),…

This paper explores the calculus of dual-valued functions and investigates the gamma function, beta function and generalized hypergeometric functions by incorporating dual numbers as parameters and variables. We examine its fundamental…

We give a combinatorial interpretation for the hypergeometric functions associated with tuples of rational numbers.

The main purpose of this paper is to compute all irreducible spherical functions on $G=\SU(3)$ of arbitrary type $\delta\in \hat K$, where $K={\mathrm{S}}(\mathrm{U}(2)\times\mathrm{U}(1))\simeq\mathrm{U}(2)$. This is accomplished by…

Many product formulas are known classically for generalized hypergeometric functions over the complex numbers. In this paper, we establish some analogous formulas for generalized hypergeometric functions over finite fields.

We discuss algorithms for arithmetic properties of hypergeometric functions. Most notably, we are able to compute the p-adic valuation of a hypergeometric function on any disk of radius smaller than the p-adic radius of convergence. This we…