Numerical integration of functions with a very small significant support

A Numerical Integration Method by Using Generalized Series of Functions

a numerical integration method by using generalized series of functions

Numerical indefinite integration of functions with singularities

We derive an indefinite quadrature formula, based on a theorem of Ganelius, for Hp functions, for p > 1, over the interval (−1, 1). The main factor in the error of our indefinite quadrature formula is O(e−π √ ), with 2N nodes and 1 p + 1 q = 1. The convergence rate of our formula is better than that of the Stenger-type formulas by a factor of √ 2 in the constant of the exponential. We conjectur...

Numerical integration of highly–oscillating functions

By a highly–oscillating function we mean one with large number of local maxima and minima over some interval. The computation of integrals of highly–oscillating functions is one of the most important issues in numerical analysis since such integrals abound in applications in many branches of mathematics as well as in other sciences, e.g., quantum physics, fluid mechanics, electromagnetics, etc....

Extrapolating Structure Functions to Very Small x

We review small x contributions to perturbative evolution equations for parton distributions, and their resummation. We emphasize in particular the resummation technique recently developed in order to deal with the apparent instability of naive small x evolution kernels and understand the empirical sucess of fixed–order perturbation theory. We give predictions for the gluon distribution and the...