Related papers: Arithmetic Constraints on Hypergeometric Identitie…
The aim of this paper is to investigate some properties, recurrence relations and identities involving degenerate hyperharmonic numbers, hyperharmonic numbers and degenerate harmonic numbers. In particular, we derive an explicit expression…
Commuting is an important property in many cases of investigation of properties of operators as well as in various applications, especially in quantum physics. Using the observation that the generalized weighted differential operator of…
A class of second-order differential equations commonly arising in physics applications are considered, and their explicit hypergeometric solutions are provided. Further, the relationship with the Generalized and Universal Associated…
I obtain new evaluations of special values of multiple polylogarithms by using a limiting case of a basic hypergeometric identity of G. E. Andrews.
We compute periods of perturbations of a Fermat variety. This allows us to consider a subspace of the Hodge cycles defined by "simple" arithmetic conditions. We explore some examples and give an upper bound for the dimension of this…
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…
Identity theorem for analytic complex functions says that a function is uniquely defined by its values on a set that contains a density point. The paper presents sufficient conditions for classes of real analytic functions that ensures…
We consider a class of weighted harmonic functions in the open upper half-plane known as $\alpha$-harmonic functions. Of particular interest is the uniqueness problem for such functions subject to a vanishing Dirichlet boundary value on the…
We prove that some of the basic differential functions appearing in the (unramified) theory of arithmetic differential equations, especially some of the basic differential modular forms in that theory, arise from a "ramified situation".…
We study the Heckman-Opdam hypergeometric functions associated to a root system of type $BC$ and a multiplicity function which is allowed to assume some non-positive values (a standard multiplicity function). For such functions, we obtain…
Given a parabolic geometry, it is sometimes possible to find special metrics characterised by some invariant conditions. In conformal geometry, for example, one asks for an Einstein metric in the conformal class. Einstein metrics have the…
The multiplicative anomaly related to the functional regularized determinants involving products of elliptic operators is introduced and some of its properties discussed. Its relevance concerning the mathematical consistency is stressed.…
We present an efficient implementation of hypergeometric functions in arbitrary-precision interval arithmetic. The functions ${}_0F_1$, ${}_1F_1$, ${}_2F_1$ and ${}_2F_0$ (or the Kummer $U$-function) are supported for unrestricted complex…
In this paper, a general integral identity for convex functions is derived. Then, we establish new some inequalities of the Simpson and the Hermite-Hadamard's type for functions whose absolute values of derivatives are convex. Some…
The notion of monogenic (or regular) functions, which is a correspondence of holomorphic functions, has been studied extensively in hypercomplex analysis, including quaternionic, octonionic, and Clifford analysis. Recently, the concept of…
Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalues, and is of practical interest because of wide range of applications in fields such as structural…
The method of rational function certification for proving terminating hypergeometric identities is extended from single sums or integrals to multi-integral/sums and ``$q$'' integral/sums.
This article is about two types of restrictions of eigenfunctions $\phi_j$ on a compact Riemannian manifold $(M,g)$: First, we restrict to a submanifold $H \subset M$, and expand the restriction $\gamma_H \phi_j$ in eigenfunctions $e_k$ of…
Let p be an odd prime. In 1984, Greene introduced the notion of hypergeometric functions over finite fields. Special values of these functions have been of interest as they are related to the number of F_p points on algebraic varieties and…
One of the most celebrated applications of Gauss' $_2F_1$ hypergeometric functions is in connection with the rapid convergence of sequences and special values that arise in the theory of arithmetic and geometric means. This theory was the…