This is the task of finding the a_jk in the expression:

There are four different ways to do this.

23.3.1 Method 1: expansion

Let

Use the constant, linear, quadratic or higher approximation to , to obtain:

.

constant, linear, quadratic or higher approximation

Example

23.3.2 Method 2: cover up

Mimic proof of theorem: ie set .

1. Deduce:

2. Set 

3. Set k = k + 1, go to step 1.

Example

23.3.3 Method 3: evaluate and solve equations

Evaluate both sides of equation (*) at r points where r is the number of unknown coefficients.

Setting the sides equal at these points give k linear equations for these unknowns.

Solve them. (Convenient points to choose are usually 0,1,-1, or near infinity.)

Example

23.3.4 Method 4: common denominator

Write both sides of (*) as polynomials ided by Q(x).

The coefficients in these polynomials of each power of x must agree; these give linear equations for the unknown. Solve them.

Example

Comment