#lang scribble/manual
@(require (for-label racket))
@title{Chebyshev Integral and Friends}
This module provides functions related to the evaluation of Chebyshev integrals
@(centered (image/plain "chebyshev.png"))
plus a few generally helpful functions.
@defproc[(chebyshev-integral [p int?]
[q (and/c int?
(>/c -1))])procedure?]{
evaluates the Chebyshev integral using integration by parts to produce a function of x.
Because of the technique used, p and q are limited to integers, and q must be non-negative.}
@defproc[(eval-over-range [a number?]
[b number?]
[f procedure?]) number?]{
returns @bold{f(b) - f(a)}, as when evaluating a definite integral. Since the
@racket[chebyshev-integral] assumes the integral constant is zero, a typical use of these
two functions might be something like
@racketblock[(let [(f (chebyshev-integral 1 2))]
(eval-over-range 0 1 f))]}
@defproc[(x^y [x number?]
[y number?]) number?]
returns @bold{x@superscript{y}}.