Related papers: Distribution evaluation of hypergeometric series
Series containing the digamma function arise when calculating the parametric derivatives of the hypergeometric functions and play a role in evaluation of Feynman diagrams. As these series are typically non-hypergeometric, a few instances…
We show that the use of generalized multivariable forms of Hermite polynomials provide an useful tool for the evaluation of families of elliptic type integrals often encountered in electrostatic and electrodynamics
Hypergraphs that can depict interactions beyond pairwise edges have emerged as an appropriate representation for modeling polyadic relations in complex systems. With the recent surge of interest in researching hypergraphs, the centrality…
We present some families of polynomials related to the moments of weight functions of hypergeometric type. We also consider different types of generating functions, and give several examples.
Partitioning a set of elements into subsets of a priori unknown sizes is essential in many applications. These subset sizes are rarely explicitly learned - be it the cluster sizes in clustering applications or the number of shared versus…
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…
We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring…
In this paper, we first establish explicit evaluations of six classes of hyperbolic sums by special values of the Gamma function by using the tools of the Fourier series expansions and the Maclaurin series expansions of a few Jacobi…
We describe the parametric behavior of the series solutions of an A-hypergeometric system. More precisely, we construct explicit stratifications of the parameter space such that, on each stratum, the series solutions of the system are…
Hypergeometric functions and their generalizations play an important r\^{o}les in diverse applications. Many authors have been established generalizations of hypergeometric functions by a number ways. In this paper, we aim at establishing…
We investigate relations between elliptic multiple zeta values and describe a method to derive the number of indecomposable elements of given weight and length. Our method is based on representing elliptic multiple zeta values as iterated…
Motivated mainly by certain interesting recent extensions of the Gamma, Beta and hypergeometric functions, we introduce here new extensions of the Beta function, hypergeometric and confluent hypergeometric functions. We systematically…
In this paper we investigate some methods on calculating the spaces of generalized semi-invariant distributions on p-adic spaces. Using homological methods, we give a criterion of automatic extension of (generalized) semi-invariant…
By means of inversion techniques and several known hypergeometric series identities, summation formulas for Fox-Wright function are explored. They give some new hypergeometric series identities when the parameters are specified.
Building on the developments of many people including Evans, Greene, Katz, McCarthy, Ono, Roberts, and Rodriguez-Villegas, we consider period functions for hypergeometric type algebraic varieties over finite fields and consequently study…
As a generalization of Riemann-Liouville integral, we introduce integral transformations of convergent power series which can be applied to hypergeometric functions with several variables.
We describe a theoretical and effective algorithm which enables us to prove that rather general hypergeometric series and integrals can be decomposed as linear combinations of multiple zeta values, with rational coefficients.
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…
General elliptic hypergeometric functions are defined by elliptic hypergeometric integrals. They comprise the elliptic beta integral, elliptic analogues of the Euler-Gauss hypergeometric function and Selberg integral, as well as elliptic…
Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases. In this paper we provide a slightly different approach toward the general problem and use it to solve one more special…