approximating sums of rational functions
Given a sum of the form where is a rational
function, it is possible to approximate it by approximating by another
rational function which can be summed in closed form. Furthermore, the
approximation so obtained becomes better as increases.
We begin with a simple illustrative example. Suppose that we want to sum
. We approximate by , which
factors as . Then, upon separating the approximate summand
into partial fractions, the sum collapses:
Using a similar approach, we may estimate the error of our approximation.
[general method to come]
Title | approximating sums of rational functions |
---|---|
Canonical name | ApproximatingSumsOfRationalFunctions |
Date of creation | 2013-03-22 18:42:23 |
Last modified on | 2013-03-22 18:42:23 |
Owner | rspuzio (6075) |
Last modified by | rspuzio (6075) |
Numerical id | 7 |
Author | rspuzio (6075) |
Entry type | Topic |
Classification | msc 41A20 |