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.
