Related papers: On a New Type Multivariable Hypergeometric Functio…
We first show that hypergeometric functions appear naturally as spectral functions when applying pseudo-differential calculus to decipher heat kernel asymptotic in the situation where the symbol algebra is noncommutative. Such observation…
We introduce a natural method of computing antiderivatives of a large class of functions which stems from the observation that the series expansion of an antiderivative differs from the series expansion of the corresponding integrand by…
Hypernetworks are neural networks that generate weights for another neural network. We formulate the hypernetwork training objective as a compromise between accuracy and diversity, where the diversity takes into account trivial symmetry…
We show how the combined use of the generating function method and of the theory of multivariable Hermite polynomials is naturally suited to evaluate integrals of gaussian functions and of multiple products of Hermite polynomials.
We describe the geometric structures involved in the variational formulation of physical theories. In presence of these structures, the constitutive set of a physical system can be generated by a family of functions. We discuss conditions,…
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…
The definition of conservative-irreversible functions is extended to smooth manifolds. The local representation of these functions is studied and reveals that not each conservative-irreversible function is given by the weighted product of…
Recently, many researchers devoted their attention to study the extensions of the gamma and beta functions. In the present work, we focus on investigating some approximations for a class of Gauss hypergeometric functions by exploiting…
Almost automorphy in the context of hyperfunctions is the main aim of this work. We give different equivalent definitions of almost automorphic hyperfunctions and then we study this class of hyperfunctions.
Ultrafunctions are a particular class of functions defined on some non- Archimedean field. They provide generalized solutions to functional equa- tions which do not have any solutions among the real functions or the distributions. In this…
In this research, Minkowski type functions which are constructed on certain probability distributions, are introduced. There are investigated differential, integral, and other properties of these functions.
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…
Markov categories, having tensors with copying and discarding, provide a setting for categorical probability. This paper uses finite colimits and what we call uniform states in such Markov categories to define a (fixed size) multiset…
In this paper we introduce the concept of \emph{multivector functionals.} We study some possible kinds of derivative operators that can act in interesting ways on these objects such as, e.g., the $A$-directional derivative and the…
In this paper, we give more general definitions of weighted means and MN-convex functions. Using these definitions, we also obtain some generalized results related to properties of MN-convex functions. The importance of this study is that…
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.
Algebras of ultradifferentiable generalized functions are introduced. We give a microlocal analysis within these algebras related to the regularity type and the ultradifferentiable property.
A specialisation of a transformation formula for multi-dimensional elliptic hypergeometric series is used to provide compact, non-determinantal formulae for the generating function with respect to the major index of standard Young tableaux…
We develop a theoretical study of non-terminating hypergeometric summations with one free parameter. Composing various methods in complex and asymptotic analysis, geometry and arithmetic of certain transcendental curves and rational…
The two most commonly used hypergeometric functions are the confluent hypergeometric function and the Gauss hypergeometric function. We review the available techniques for accurate, fast, and reliable computation of these two hypergeometric…