An Alternate Method for Finding the Partial Fraction Decomposition of a Rational Function

1984 ◽  
Vol 91 (6) ◽  
pp. 365 ◽  
Author(s):  
H. Joseph Straight ◽  
Richard Dowds
Keyword(s):  
Rational Function ◽  
Partial Fraction ◽  
Partial Fraction Decomposition

scholarly journals A Binomial Coefficient Identity Associated with Beukers' Conjecture on Apéry numbers

10.37236/1856 ◽  
2004 ◽  
Vol 11 (1) ◽  
Author(s):  
Wenchang Chu
Keyword(s):  
Rational Function ◽  
Binomial Coefficient ◽  
Harmonic Number ◽  
Partial Fraction ◽  
Algebraic Identity ◽  
Apéry Numbers ◽  
Partial Fraction Decomposition ◽  
Limiting Case ◽  
Binomial Coefficient Identity

By means of partial fraction decomposition, an algebraic identity on rational function is established. Its limiting case leads us to a harmonic number identity, which in turn has been shown to imply Beukers' conjecture on the congruence of Apéry numbers.

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.

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