Related papers: Integration in terms of polylogarithm
In a recent paper, D. Harlow, J. Maltz, and E. Witten showed that a particular proposal for the timelike Liouville three-point function, originally due to Al. Zamolodchikov and to I. Kostov and V. Petkova, can actually be computed by the…
The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the design of objects exhibiting that behavior in engineering.…
A method of integrable discretization of the Liouville type nonlinear partial differential equations is suggested based on integrals. New examples of discrete Liouville type models are presented.
We obtain a new decomposition of the Riemann-Liouville operators of fractional integration as a series involving derivatives (of integer order). The new formulas are valid for functions of class $C^n$, $n \in \mathbb{N}$, and allow us to…
The main aim of this paper is to establish several Landau-type theorems for certain bounded poly-analytic functions and reduced poly-analytic functions that generalize some previously established results.
The purpose of this manuscript is to derive two distinct integral representations of the generalized polylogarithm using two different techniques. The first approach involves the Dirichlet series and its Laplace representation, which leads…
Suggestions concerning the generalization of the geometric quantization to the case of nonlinear field theories are given. Results for the Liouville field theory are presented.
Multiple elliptic polylogarithms can be written as (multiple) integrals of products of basic hypergeometric functions. The latter are computable, to arbitrary precision, using a q-difference equation and q-contiguous relations.
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed.
A new form of a binary Darboux transformation is used to generate analytical solutions of a nonlinear Liouville-von Neumann equation. General theory is illustrated by explicit examples.
We give applications of known and new Liouville type theorems to universal singularity and decay estimates for non scale invariant elliptic problems, including Lane-Emden and Schr\"odinger type systems. This applies to various classes of…
Using a concept of filter we propose one generalization of Riemann integral, that is integration with respect to filter. We study this problem, demonstrate different properties and phenomena of filter integration.
A Liouville classification of a natural Hamiltonian system on the projective plane with a rotation metric and a linear integral is obtained. All Fomenko--Zieschang invariants (i.e., labeled molecules) of the system are calculated.
Here the polynomial interpolation approach is used to introduce the main results on multivariate normal algebraic systems. Next we bring a construction which shows that any standard algebraic system, with finite set of solutions, can be…
An arbitrary-depth reduction theorem for the `convolution' multiple L-values of Euler-Zagier type is proven by an analytic method. To this end, generalized polylogarithms associated to Dirichlet characters are defined. The proof uses the…
This document is a companion for the Maple program \textbf{Summing a polynomial function over integral points of a polygon}. It contains two parts. First, we see what this programs does. In the second part, we briefly recall the…
This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.
The post-Newtonian approximation of general relativistic Liouville's equation is presented. Two integrals of it, generalizations of the classical energy and angular momentum, are obtained. Polytropic models are constructed as an…
In this paper, we are concerned with a Liouville-type result of the nonlinear integral equation \begin{equation*} u(x)=\int_{\mathbb{R}^{n}}\frac{u(1-|u|^{2})}{|x-y|^{n-\alpha}}dy, \end{equation*} where $u: \mathbb{R}^{n} \to…
Neville's algorithm is known to provide an efficient and numerically stable solution for polynomial interpolations. In this paper, an extension of this algorithm is presented which includes the derivatives of the interpolating polynomial.