## ABSTRACT

CHAPTER 10

10.1. Introduction

The table of integrals [35] contains a large variety of definite integrals that can be evaluated by expanding the integrand. The idea is remarkably simple: to evaluate

(10.1.1) I =

f(x) dx,

one chooses a set of functions {fn : n ∈ N } for which it is possible to expand

(10.1.2) f(x) =

anfn

uniformly on [a, b]. Then, with

(10.1.3) bn =

fn(x) dx,

it follows that

(10.1.4)

f(x) dx =

anbn.