相关论文: An example of Feynman-Jackson integral

Following an idea due to J. Bernoulli, we explore the q-analogue of the sums of powers of consecutive integers.

We introduce a technique for handling Whitney decompositions in Gaussian harmonic analysis and apply it to the study of Gaussian analogues of the classical tent spaces $T^{1,q}$ of Coifman, Meyer and Stein.

I present a $q$-analog of the discrete Painlev\'e I equation, and a special realization of it in terms of $q$-orthogonal polynomials.

In this work we discuss techniques for the numerical computation of Fox functions that represent Feynman integrals. Illustrative examples based on Sinc numerical methods and Quasi-Monte Carlo methods are given

In this paper, we present the (p; q)-analogues of some inequalities concerning the digamma function. Our results generalize some earlier results.

The Gaussian integral, denoted as \( \int_{-\infty}^{\infty} e^{-x^2} dx \), plays a significant role in mathematical literature. In this paper, we explore a family of integrals related to Gaussian functions. Specifically, we introduce…

In this paper we show that in the presence of torsion and a metric with an antisymmetric part one can construct a gravitational analog of Faraday's law of electromagnetism.

I discuss a progress in calculations of Feynman integrals based on the Gegenbauer Polynomial Technique and the Differential Equation Method.

A new method for approximating fractional derivatives of the Gaussian function and Dawson's integral are presented. Unlike previous approaches, which are dominantly based on some discretization of Riemann-Liouville integral using polynomial…

The universal method of expansion of integrals is suggested. It allows in particular to derive the threshold expansion of Feynman integrals.

We give q-analogues of Wilson's theorem for the primes congruent 1 and 3 modulo 4 respectively. And q-analogues of two congruences due to Mordell and Chowla are also established.

A connection between one-loop $N$-point Feynman diagrams and certain geometrical quantities in non-Euclidean geometry is discussed. A geometrical way to calculate the corresponding Feynman integrals is considered. (This paper contains a…

We define an overpartition analogue of Gaussian polynomials (also known as $q$-binomial coefficients) as a generating function for the number of overpartitions fitting inside the $M \times N$ rectangle. We call these new polynomials over…

We give a new $q$-$(1+q)$-analogue of the Gaussian coefficient, also known as the $q$-binomial which, like the original $q$-binomial $\genfrac{[}{]}{0pt}{}{n}{k}_{q}$, is symmetric in $k$ and $n-k$. We show this $q$-$(1+q)$-binomial is more…

A Feymnan integral is computed exactly using LLL

We introduce a symbolic method for the evaluation of definite integrals containing combinations of various functions, including exponentials, logarithm and products of Bessel functions of different types. The method we develop is naturally…

In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried…

In this paper we construct the $q$-analogue of Barnes's Bernoulli numbers and polynomials of degree 2, for positive even integers, which is an answer to a part of Schlosser's question. For positive odd integers, Schlosser's question is…

In this paper a double integral containing two Gaussian hypergeometric functions is discussed. The integral is not found in the literature and a direct computation is not (yet) possible. Therefore, a complete different integral is computed…

We study some graded geometric constructions appearing naturally in the context of gauge theories. Inspired by a known relation of gauging with equivariant cohomology we generalize the latter notion to the case of arbitrary Q-manifolds…