scholarly journals A new identity via partial fraction decomposition

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1957-1967
Author(s):  
Ji-Ke Ge ◽  
Tao-Tao Liu ◽  
Qiu-Ming Luo
Keyword(s):  
Partial Fraction ◽  
Partial Fraction Decomposition ◽  
Binomial Identities

In this paper, we obtain a new identity using the partial fraction decomposition. As applications, some interesting binomial identities are also derived.

Evaluation of sums involving products of Gaussian q-binomial coefficients with applications

2019 ◽  
Vol 69 (2) ◽  
pp. 327-338 ◽  
Author(s):  
Emrah Kiliç ◽  
Helmut Prodinger
Keyword(s):  
Weight Function ◽  
Binomial Coefficients ◽  
Partial Fraction ◽  
Partial Fraction Decomposition ◽  
Sums Of Products ◽  
Binomial Identities

Abstract Sums of products of two Gaussian q-binomial coefficients, are investigated, one of which includes two additional parameters, with a parametric rational weight function. By means of partial fraction decomposition, first the main theorems are proved and then some corollaries of them are derived. Then these q-binomial identities will be transformed into Fibonomial sums as consequences.

scholarly journals Binomial symmetries inspired by Bruckman's problem

Filomat ◽  
2010 ◽  
Vol 24 (1) ◽  
pp. 41-46 ◽  
Author(s):  
Wenchang Chu ◽  
Ying You
Keyword(s):  
Decomposition Method ◽  
Partial Fraction ◽  
Subject Classifications ◽  
Special Cases ◽  
Secondary 05A30 ◽  
Primary 05A10 ◽  
Partial Fraction Decomposition ◽  
Mathematics Subject Classifications ◽  
Binomial Identities

The partial fraction decomposition method is employed to establish two general algebraic identities, which contain consequently several binomial identities and their q-analogues as special cases. 2010 Mathematics Subject Classifications. Primary 05A10; Secondary 05A30. .

scholarly journals Two-loop leading colour QCD corrections to $$ q\overline{q} $$ → γγg and qg → γγq

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Bakul Agarwal ◽  
Federico Buccioni ◽  
Andreas von Manteuffel ◽  
Lorenzo Tancredi
Keyword(s):  
Numerical Code ◽  
Tree Level ◽  
Partial Fraction ◽  
Integration By Parts ◽  
Analytic Expressions ◽  
Partial Fraction Decomposition ◽  
Loop Amplitudes

Abstract We present the leading colour and light fermionic planar two-loop corrections for the production of two photons and a jet in the quark-antiquark and quark-gluon channels. In particular, we compute the interference of the two-loop amplitudes with the corresponding tree level ones, summed over colours and polarisations. Our calculation uses the latest advancements in the algorithms for integration-by-parts reduction and multivariate partial fraction decomposition to produce compact and easy-to-use results. We have implemented our results in an efficient C++ numerical code. We also provide their analytic expressions in Mathematica format.

scholarly journals Rational Solutions of Riccati Differential Equation with Coefficients Rational

2011 ◽  
Vol 2011 ◽  
pp. 1-44
Author(s):  
Nadhem Echi
Keyword(s):  
Differential Equation ◽  
Galois Group ◽  
Efficient Method ◽  
Rational Solution ◽  
Partial Fraction ◽  
Rational Solutions ◽  
Riccati Differential Equation ◽  
Differential Galois Group ◽  
Partial Fraction Decomposition ◽  
Decomposition Of Solution

This paper presents a simple and efficient method for determining the rational solution of Riccati differential equation with coefficients rational. In case the differential Galois group of the differential equation , is reducible, we look for the rational solutions of Riccati differential equation , by reducing the number of checks to be made and by accelerating the search for the partial fraction decomposition of the solution reserved for the poles of which are false poles of . This partial fraction decomposition of solution can be used to code . The examples demonstrate the effectiveness of the method.

Parallel Solution of Linear Systems

2016 ◽  
Vol 6 (3) ◽  
pp. 278-289
Author(s):  
Sidi-Mahmoud Kaber ◽  
Amine Loumi ◽  
Philippe Parnaudeau
Keyword(s):  
Linear Systems ◽  
Numerical Algorithms ◽  
Parallel Architecture ◽  
Decomposition Methods ◽  
Partial Fraction ◽  
Domain Decomposition Methods ◽  
Simple Method ◽  
Parallel Solution ◽  
Partial Fraction Decomposition ◽  
Programming Paradigms

AbstractComputational scientists generally seek more accurate results in shorter times, and to achieve this a knowledge of evolving programming paradigms and hardware is important. In particular, optimising solvers for linear systems is a major challenge in scientific computation, and numerical algorithms must be modified or new ones created to fully use the parallel architecture of new computers. Parallel space discretisation solvers for Partial Differential Equations (PDE) such as Domain Decomposition Methods (DDM) are efficient and well documented. At first glance, parallelisation seems to be inconsistent with inherently sequential time evolution, but parallelisation is not limited to space directions. In this article, we present a new and simple method for time parallelisation, based on partial fraction decomposition of the inverse of some special matrices. We discuss its application to the heat equation and some limitations, in associated numerical experiments.

scholarly journals Auotomodeling rational mnemofunctions and their link to an analytical representation of distributions

2019 ◽  
Vol 55 (3) ◽  
pp. 288-298
Author(s):  
T. R. Shahava
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Expansions ◽  
Real Line ◽  
Analytical Representation ◽  
Partial Fraction ◽  
Boundary Values ◽  
Multiplication Rule ◽  
Space Of Distributions ◽  
Partial Fraction Decomposition ◽  
Proper Rational Function

Mnemofunctions of the form f(x/ε), where f is the proper rational function without singularities on the real line, are considered in this article. Such mnemofunctions are called automodeling rational mnemofunctions. They possess the following fine properties: asymptotic expansions in the space of distributions can be written in explicit form and the asymptotic expansion of the product of such mnemofunctions is uniquely determined by the expansions of multiplicands.Partial fraction decomposition of automodeling rational mnemofunctions generates the so-called sloped analytical representation of a distribution, i.e. the representation of a distribution by a jump of the boundary values of the functions analytical in upper and lower half-planes. Sloped analytical representation is similar to the classical Cauchy analytical representation, but its structure is more complicated. The multiplication rule of such representations is described in this article.

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