Related papers: Elliptic hypergeometric functions: integrals versu…
The classical beta function B(x; y) is one of the most fundamental special functions, due to its important role in various fields in the mathematical, physical, engineering and statistical sciences. Useful extensions of the classical Beta…
For an elliptic curve $E$ defined over a field $k\subset \mathbb C$, we study iterated path integrals of logarithmic differential forms on $E^\dagger$, the universal vectorial extension of $E$. These are generalizations of the classical…
In this article we give evaluations of certain series of hyperbolic functions, using Jacobi elliptic functions theory. We also define some new functions that enable us to give characterization of not solvable class of series.
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…
The Euler-MacLaurin summation formula relates a sum of a function to a corresponding integral, with a remainder term. The remainder term has an asymptotic expansion, and for a typical analytic function, it is a divergent (Gevrey-1) series.…
By making use of some techniques based upon certain inverse new pairs of symbolic operators, the author investigate several decomposition formulas associated with Humbert hypergeometric functions $\Phi_1 $, $\Phi_2 $, $\Phi_3 $, $\Psi_1 $,…
We show that gauge-independent terms in the one-loop and multi-loops $\beta$-functions of the Standard Model can be exactly computed from the Wetterich functional renormalization of a matrix model. Our framework is associated to the finite…
One-dimensional and two-dimensional integrals containing $E_b(-u)$ and $E_{\alpha ,\beta }\left(\delta x^{\gamma }\right)$ are considered. $E_b(-u)$ is the Mittag-Leffler function and the integral is taken over the rectangle $0 \leq x <…
We show that indefinite theta series on cones converge and provide an explicit modular completion. Our completion rests on a convolution of the Gaussian with a piecewise constant function supported on the cone. Our main innovation is to…
In this paper, we investigate the Euler-type integral representations for the generalized hypergeometric matrix function and develop some transformations in terms of hypergeometric matrix functions. Furthermore, unit and half arguments have…
A Petrov-Galerkin finite element method is constructed for a singularly perturbed elliptic problem in two space dimensions. The solution contains a regular boundary layer and two characteristic boundary layers. Exponential splines are used…
We introduce a generalization of elliptic 6j-symbols, which can be interpreted as matrix elements for intertwiners between corepresentations of Felder's elliptic quantum group. For special parameter values, they can be expressed in terms of…
In this paper we shall investigate the problem of the representation of the number of integral points of an elliptic curve modulo a prime number p. We present a way of expressing an exponential sum which involves polynomials of third…
We prove analogues for elliptic interpolation functions of Macdonald's version of the Littlewood identity for (skew) Macdonald polynomials, in the process developing an interpretation of general elliptic "hypergeometric" sums as skew…
We introduce and study "elliptic zeta values", a two-parameter deformation of the values of Riemann's zeta function at positive integers. They are essentially Taylor coefficients of the logarithm of the elliptic gamma function, and share…
We describe an effective method for calculating certain infinite sums, generalizations of the classical Bernoulli polynomials. As shown by Edward Witten in his papers on two-dimensional gauge theories, the correlation functions of…
This paper investigates a class of special Berndt-type integral calculations where the integrand contains only hyperbolic cosine functions. The research approach proceeds as follows: Firstly, through contour integration methods, we…
We find new representations for Itzykson-Zuber like angular integrals for arbitrary beta, in particular for the orthogonal group O(n), the unitary group U(n) and the symplectic group Sp(2n). We rewrite the Haar measure integral, as a flat…
By a real alphabeta-geometry we mean a four-dimensional manifold M equipped with a neutral metric h such that (M,h) admits both an integrable distribution of alpha-planes and an integrable distribution of beta-planes. We obtain a local…
Our purpose in this present paper is to investigate generalized integration formulas containing the extended generalized hypergeometric function and obtained results are expressed in terms of extended hypergeometric function. Certain…