Related papers: Distribution evaluation of hypergeometric series

There are many identities for the hypergeometric series presented in the article "Special values of the hypergeometric series" by Ebisu. In this note, we obtain a new hypergeometric identity, which includes some of these identities as…

We provide several properties of the geometric polynomials discussed in earlier works of the authors. Further, the geometric polynomials are used to obtain a closed form evaluation of certain series involving Riemann's zeta function.

In the last few years there has been a growing interest towards methods for statistical inference and learning based on computational geometry and, notably, tropical geometry, that is, the study of algebraic varieties over the min-plus…

We explicitly construct a class of multivariate generalized hypergeometric series which is conjectured in our previous paper [Alkalaev & Mandrygin 2025] to calculate multipoint one-loop parametric conformal integrals in $D$ dimensions. Our…

We prove a summation formula for a bilateral series whose terms are products of two basic hypergeometric functions. In special cases, series of this type arise as matrix elements of quantum group representations.

An approach to modeling the oligomer composition distribution function in the irreversible step growth homopolymerization process based on a mixture of oligomers of arbitrary composition is developed. The approach is based on consideration…

High-dimensional group inference is an essential part of statistical methods for analysing complex data sets, including hierarchical testing, tests of interaction, detection of heterogeneous treatment effects and inference for local…

We suggest a new approach to the study of relatively hyperbolic groups based on relative isoperimetric inequalities. Various geometric, algebraic, and algorithmic properties are discussed.

This paper discusses certain properties of heterogeneous hypergeometric functions with two matrix arguments. These functions are newly defined but have already appeared in statistical literature and are useful when dealing with the…

In this paper, we define a new type multivariable hypergeometric function. Then, we obtain some generating functions for these functions. Furthermore, we derive various families of multilinear and multilateral generating functions for these…

We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…

By dividing hypergeometric series representations of the inverse sine by sin^-1 (x) and integrating, new double series representations of integers and constants arise. Binomial coefficients and the sine integral are thus combined in double…

We study values of generalized polylogarithms at various points and relationships among them. Polylogarithms of small weight at the points 1/2 and -1 are completely investigated. We formulate a conjecture about the structure of the linear…

We elaborate on the expansion of hypergeometric functions about rational parameters, where we focus mainly on the integer and half-integer case. The strategy and the basic steps of a recently developed algorithm for the expansion about…

We construct bases for the spaces of higher order modular forms of all orders and weights. We also provide a cohomological interpretation of these forms.

We discuss how generalized multiresolution analyses (GMRAs), both classical and those defined on abstract Hilbert spaces, can be classified by their multiplicity functions $m$ and matrix-valued filter functions $H$. Given a natural number…

We examine the convergence of $q$-hypergeometric series when $|q|=1$.

We use a simple method to derive two concentration bounds on the hypergeometric distribution. Comparison with existing results illustrates the advantage of these bounds across different regimes.

Hypergeometric class equations are given by second order differential operators in one variable whose coefficient at the second derivative is a polynomial of degree $\leq2$, at the first derivative of degree $\leq1$ and the free term is a…

By systematically applying ten inequivalent two-part relations between hypergeometric sums 3F2(1) to the published database of all such sums, 66 new sums are obtained. Many results extracted from the literature are shown to be special cases…