Related papers: Finite hypergeometric functions
We will present some (formal) arguments that any Feynman diagram can be understood as a particular case of a Horn-type multivariable hypergeometric function. The advantages and disadvantages of this type of approach to the evaluation of…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
We report on implementations for algorithms treating algebraic and arithmetic properties of hypergeometric functions in the computer algebra system SageMath. We treat hypergeometric series over the rational numbers, over finite fields, and…
The main goal of this paper is to derive a number of identities for the generalized hypergeometric function evaluated at unity and for certain terminating multivariate hypergeometric functions from the symmetries and other properties of…
General theory of elliptic hypergeometric series and integrals is outlined. Main attention is paid to the examples obeying properties of the "classical" special functions. In particular, an elliptic analogue of the Gauss hypergeometric…
Without leaving finite mathematics and using finite topological spaces only, we give a definition of homeomorphisms of finite abstract simplicial complexes or finite graphs. Besides exploring the definition in various contexts, we add some…
In this note, we firstly establish an extended Gauss's summation identity. Using this identity, we compute values of a family of $_4F_3$ hypergeometric functions, which generalize the results obtained by Ferretti et al..
Let $X$ be an algebraic variety over a finite field $\bF_q$, homogeneous under a linear algebraic group. We show that the number of rational points of $X$ over $\bF_{q^n}$ is a periodic polynomial function of $q^n$ with integer…
Moments for hypergeometric functions over finite fields were studied in the work of Ono, Pujahari, Saad, and Saikia for several $_{2}F_{1}$ and $_{3}F_{2}$ cases. We generalize their work to prove results for new cases where the…
In this manuscript, we investigate some properties of certain counting functions, associated to the ergodic sums computed along the periodic orbits of the skew-product map, related to a finitely generated rational semigroup. To be precise,…
We study the action of Hecke operators on the set of hypergeometric functions. We show that the spectrum of these operators is the set of powers n^a and that polylogarithms play a dominant role in the study of the corresponding…
This article gives a brief introduction to $q$-special functions, i.e., $q$-analogues of the classical special functions. Here $q$ is a deformation parameter, usually $0<q<1$, where $q=1$ is the classical case. The main topics to be treated…
In this paper, we study some extended hypergeometric functions from matrix point of view. We have given the integral representations of these matrix functions. Finally, we obtain some generating function relations using fractional…
Hypergeometric equations with a dihedral monodromy group can be solved in terms of elementary functions. This paper gives explicit general expressions for quadratic monodromy invariants for these hypergeometric equations, using a…
We define a function in terms of quotients of the $p$-adic gamma function which generalizes earlier work of the author on extending hypergeometric functions over finite fields to the $p$-adic setting. We prove, for primes $p > 3$, that the…
Hypergeometric functions of one and many variables play an important role in various branches of modern physics and mathematics. Often we have hypergeometric functions with indices linear dependent on a small parameter with respect to which…
We obtain new inequalities for certain hypergeometric functions. Using these inequalities, we deduce estimates for the hyperbolic metric and the induced distance function on a certain canonical hyperbolic plane domain.
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
The goal of this paper is to explain how a simple but apparently new fact of linear algebra together with the cohomological interpretation of L-functions allows one to produce many examples of L-functions over function fields vanishing to…
We calculate some finite and infinite sums containing the digamma function in closed-form. For this purpose, we differentiate selected reduction formulas of the hypergeometric function with respect to the parameters applying some derivative…