In the article, the noted Darboux’s formula of functions with single variable is generalized to that of functions of two independent variables with integral remainder, some important special cases of Darboux’s formula of functions with two variables are obtained, and some estimates of the integral remainders and Darboux’s expansion of the function ln(x + y) are given. These results generalize A...

ABSTRACT A scheme for systematically separating ultraviolet divergences of Feynrnan amplitudes in parametric space is developed. It is summarized by an explicit formula which enables us to incorporate readily the ultraviolet-finite remainders thus constructed into the usual renormalization s theme . It is shown further that infrared divergences can be treated in a very similar way. Our method i...

The authors have implemented three numerical quadrature schemes, using the Arbitrary Precision (ARPREC) software package. The objective here is a quadrature facility that can efficiently evaluate to very high precision a large class of integrals typical of those encountered in experimental mathematics, relying on a minimum of a priori information regarding the function to be integrated. Such a ...

We take a pragmatic approach to numerical integration of unbounded functions. In this context we discuss and evaluate the practical application of a method suited also for non-specialists and application developers. We will show that this method can be applied to a rich body of functions, and evaluate it's merits in comparison to other methods for integration of unbounded integrals. Furthermore...

Calculations of observables in Quantum Chromodynamics are typically performed using a method that combines numerical integrations over the momenta of final state particles with analytical integrations over the momenta of virtual particles. I discuss a method for performing all of the integrations