Related papers: Numerical Evaluation of Generalized Hypergeometric…
We provide a complete classification of the algebraicity of (generalized) hypergeometric functions with no restriction on the set of their parameters. Our characterization relies on the interlacing criteria of Christol (1987) and…
Potential functions can be used as generating potentials of relevant geometric structures for a Riemannian manifold such as the Riemannian metric and affine connections. We study wether this procedure can also be applied to tensors of rank…
The functional relation of the Hurwitz zeta function is proved by using the connection problem of the confluent hypergeometric equation.
We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…
We offer some summation formulas that appear to have great utility in probability theory. The proofs require some recent results from analysis that have thus far been applied to basic hypergeometric functions.
The main objective of this work is to describe a general and original approach for computing an off-line solution for a set of parameters describing the geometry of the domain. That is, a solution able to include information for different…
We review "creative" strategies of closed-form evaluations of hypergeometric functions.
The number of linear independent algebraic relations among elementary symmetric polynomial functions over finite fields is computed. An algorithm able to find all such relations is described. It is proved that the basis of the ideal of…
In this paper, we propose a general method to express explicitly the inversion and the connection coefficients between two basic hypergeometric polynomial sets. As application, we consider some $d$-orthogonal basic hypergeometric…
Graph matching is an important and persistent problem in computer vision and pattern recognition for finding node-to-node correspondence between graph-structured data. However, as widely used, graph matching that incorporates pairwise…
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…
Decomposition formulas associated with the Lauricella multivariable hypergeometric functions were known, however, due to the recurrence of those formulas, additional difficulties may arise in the applications. Further study of the…
In this paper, we present HyperPrecision, a Mathematica package for high-precision numerical evaluation of general Horn-type multivariate hypergeometric functions and their Laurent expansions in a small parameter $\epsilon$. Such functions…
We review the series solutions of the general and single-confluent Heun equations in terms of powers, ordinary-hypergeometric and confluent-hypergeometric functions. The conditions under which the expansions reduce to finite sums as well as…
The Whittaker function and its diverse extensions have been actively investigated. Here we introduce an extension of the Whittaker function by using the known extended confluent hypergeometric function $\Phi_{p,v}$ and investigate some of…
The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear…
The relationship between Feynman diagrams and hypergeometric functions is discussed. Special attention is devoted to existing techniques for the construction of the $\epsilon$-expansion. As an example, we present a detailed discussion of…
In this paper, we consider sums of values of degenerate falling factorials and give a probabilistic proof of a recurrence relation for them. This may be viewed as a degenerate version of the recent probabilistic proofs on sums of powers of…
Using matrix inversion and determinant evaluation techniques we prove several summation and transformation formulas for terminating, balanced, very-well-poised, elliptic hypergeometric series.
The confluent hypergeometric point process represents a universality class which arises in a variety of different but related areas. It particularly describes the local statistics of eigenvalues in the bulk of spectrum near a Fisher-Hartwig…