Related papers: Numerical Evaluation of Generalized Hypergeometric…
We introduce methods for obtaining pretrained Geometric Neural Operators (GNPs) that can serve as basal foundation models for use in obtaining geometric features. These can be used within data processing pipelines for machine learning tasks…
We are going to study properties of "hypergeometrization" -- an operator which act on analytic functions near the origin by inserting two Pochhammer symbols into their Taylor series. In essence, this operator maps elementary function into…
The degeneration of the hyperelliptic sigma function is studied. We use the Sato Grassmannian for this purpose. A simple decomposition of a rational function gives a decomposition of Pl\"ucker coordinates of a frame of the Sato…
In this article, we show a new general linear independence criterion related to values of $G$-functions, including the linear independence of values at algebraic points of contiguous hypergeometric functions, which is not known before. Let…
Several new relationships between hypergeometric functions are found by comparing results for Feynman integrals calculated using different methods. A new expression for the one-loop propagator-type integral with arbitrary masses and…
We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…
This article presents a survey of work on lifted graphical models. We review a general form for a lifted graphical model, a par-factor graph, and show how a number of existing statistical relational representations map to this formalism. We…
Hypergeometric structures in single and multiscale Feynman integrals emerge in a wide class of topologies. Using integration-by-parts relations, associated master or scalar integrals have to be calculated. For this purpose it appears useful…
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 efficient methods for calculating linear recurrences of hypergeometric double sums and, more generally, of multiple sums. In particular, we supplement this approach with the algorithmic theory of contiguous relations, which…
We describe here an experimental method that permits to compute a good candidate for the closed form of a generating function if we know the first few terms of a series. The method is based on integer relations algorithms and uses either…
We obtain new recurrence relations, an explicit formula, and convolution identities for higher order geometric polynomials. These relations generalize known results for geometric polynomials, and lead to congruences for higher order…
A simple algorithm with quasi-linear time complexity and linear space complexity for the evaluation of the hypergeometric series with rational coefficients is constructed. It is shown that this algorithm is suitable in practical informatics…
The main aim of the present work is to give some interesting the $q$-analogues of various $q$-recurrence relations, $q$-recursion formulas, $q$-partial derivative relations, $q$-integral representations, transformation and summation…
This paper introduces deep Gaussian processes (DGPs) for geophysical parameter retrieval. Unlike the standard full GP model, the DGP accounts for complicated (modular, hierarchical) processes, provides an efficient solution that scales well…
The hypergeometric distribution is a popular distribution, whose properties have been extensively investigated. Generating functions of this distribution, such as the probability-generating function, the moment-generating function, and the…
The monodromy of hypergeometric functions can govern the properties of the functions themselves. Previously, the second and third authors studied the commensurability relations among monodromy groups of the Appell--Lauricella hypergeometric…
For an odd prime $p$, let $\phi$ denote the quadratic character of the multiplicative group ${\mathbb F}_p^\times$, where ${\mathbb F}_p$ is the finite field of $p$ elements. In this paper, we will obtain evaluations of the hypergeometric…
We prove two transformations for the $p$-adic hypergeometric functions which can be described as $p$-adic analogues of a Euler's transformation and a transformation of Clausen. We first evaluate certain character sums, and then relate them…
Kamp\'e de F\'eriet hypergeometric functions are two-variable hypergeometric functions, which are a generalization of Appell's functions. It is known that they satisfy many reduction and summation formulas. In this paper, we define Kamp\'e…