Related papers: (Strange) gamma evaluations
In this short survey article, we showcase a number of non-trivial geometric problems that have recently been resolved by marrying methods from functional calculus and real-variable harmonic analysis. We give a brief description of these…
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 prove hypergeometric type summation identities for a function defined in terms of quotients of the $p$-adic gamma function by counting points on certain families of hyperelliptic curves over $\mathbb{F}_{q}$. We also find certain special…
We consider a certain definite integral involving the product of two classical hypergeometric functions having complicated arguments. We show in this paper the surprising fact that this integral does not depend on the parameters of the…
The incomplete beta function is an important special function in statistics. In modern theory of hypergeometric functions, we regard hypergeometric functions as pairings of twisted cycles and twisted cocycles. However, the incomplete beta…
We define a special function related to the digamma function and use it to evaluate in closed form various series involving binomial coefficients and harmonic numbers.
We use the fermionic construction of two-matrix model partition functions to evaluate integrals over rational symmetric functions. This approach is complementary to the one used in the paper ``Integrals of Rational Symmetric Functions,…
We study varieties defined over nonstandard fields using techniques of nonstandard mathematics.
We propose a generating functional for nonrelativistic gauge invariant actions. In particular, we consider actions without the usual magnetic term. Like in the Born-Infeld theory, there is an upper bound to the electric field strength in…
We define a number of natural (from geometric and combinatorial points of view) deformation spaces of valuations on finite graphs, and study functions over these deformation spaces. These functions include both direct metric invariants…
We summarize recent results initiating spectral analysis on pseudo-Riemannian locally symmetric spaces $\Gamma \backslash G/H$, beyond the classical setting where $H$ is compact (e.g. theory of automorphic forms for arithmetic $\Gamma$) or…
We present explicit representations in terms of hypergeometric functions for the scaling functions in the $C^0$ orthogonal multiresolution analyses associated with piecewise continuous polynomials. Closed formulas for the Mellin transform…
We give a closed form for $quotients$ of truncated basic hypergeometric series where the base $q$ is evaluated at roots of unity.
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…
We examine hypergeometric functions in the finite field, p-adic and classical settings. In each setting, we prove a formula which splits the hypergeometric function into a sum of lower order functions whose arguments differ by roots of…
The alternative approach to QCD analysis of the structure function F2gamma is presented. It differs from the conventional one by the presence of the terms, which in conventional approach appear in higher orders. The numerical results show…
We provide a new algorithm for evaluating the gamma function at any (rational) point and a new infinite product representation free from the presence of Euler and Mascheroni constant.Formulae and inequalities seemingly new are obtained as…
For certain class of hypergeometric functions ${}_3F_2$ with rational parameters, we give a sufficient condition for the special value at $1$ to be expressed in terms of logarithms of algebraic numbers. We give two proofs, both of which are…
The beta integral method proved itself as a simple nonetheless powerful method of generating hypergeometric identities at a fixed argument. In this paper we propose a generalization by substituting the beta density with a particular type of…
We give the hypergeometric solutions of some algebraic equations including the general fifth degree equation.