Related papers: Incomplete A-Hypergeometric Systems
Finite hypergeometric functions are functions of a finite field ${\bf F}_q$ to ${\bf C}$. They arise as Fourier expansions of certain twisted exponential sums and were introduced independently by John Greene and Nick Katz in the 1980's.…
We review Aomoto's generalized hypergeometric functions on Grassmannian spaces Gr(k +1, n+1). Particularly, we clarify integral representations of the generalized hypergeometric functions in terms of twisted homology and cohomology. With an…
The established technique of eliminating upper or lower parameters in a general hypergeometric series is profitably exploited to create pathways among confluent hypergeometric functions, binomial functions, Bessel functions, and exponential…
In this paper, we present an extension of Mittag-Leffler function by using the extension of beta functions (\"{O}zergin et al. in J. Comput. Appl. Math. 235 (2011), 4601-4610) and obtain some integral representation of this newly defined…
The perturbative $\beta$-function is known exactly in a number of supersymmetric theories and in the 't Hooft renormalization scheme in the $\phi_4^4$ model. It is shown how this allows one to compute the effective action exactly for…
Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams.…
The variable change w=exp(u) is applied to establish novel integral representations of the incomplete gamma-function, hypergeometric F-function,confluent hypergeometric /Phi-function and beta-function, and to analyze these functionsas as…
A general criterion is given for the vanishing of the beta-functions in N=1 supersymmetric gauge theories.
Functional digraphs are unlabelled finite digraphs where each vertex has exactly one out-neighbor. They are isomorphic classes of finite discrete-time dynamical systems. Endowed with the direct sum and product, functional digraphs form a…
We determine the asymptotic behaviour of certain incomplete Betafunctions.
The authors survey recent results in special functions, particularly the gamma function and the Gaussian hypergeometric function.
We define a general class of (multiple) integrals of hypergeometric type associated with the Jacobi theta functions. These integrals are related to theta hypergeometric series through the residue calculus. In the one variable case, we get…
The set of associative and commutative hypercomplex numbers, called the perfect hypercomplex algebra (PHA) is investigated. Necessary and sufficient conditions for an algebra to be a PHA via semi-tensor product(STP) of matrices are…
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…
In this paper, we use some standard numerical techniques to approximate the hypergeometric function $$ {}_2F_1[a,b;c;x]=1+\frac{ab}{c}x+\frac{a(a+1)b(b+1)}{c(c+1)}\frac{x^2}{2!}+\cdots $$ for a range of parameter triples $(a,b,c)$ on the…
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 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…
We consider the problem of determining the beta-functions for any reduced effective field theory. Even though not all the Green's functions of a reduced effective field theory are renormalizable, unlike the full effective field theory,…
Feynman integrals that have been evaluated in dimensional regularization can be written in terms of generalized hypergeometric functions. It is well known that properties of these functions are revealed in the framework of intersection…
The partition function of an N=2 gauge theory in the Omega-background satisfies, for generic value of the parameter beta=-eps_1/eps_2, the, in general extended, but otherwise beta-independent, holomorphic anomaly equation of special…