Module 7: Multistep Methods
  Lecture 24: Special 2nd order equations(Contd.)
 

 

we obtain

(7.52)

where

(7.53)

The generating function is given as:

on integration, we find

(7.54)

The recurrence relation is obtained as

By comparing (7.50) and (7.54), we also find that

The numerical values of are readily found as follows:

m

0

1

2

3

4

5

6

4

-8

0

For (7.52) has an irregular appearance, and its use for practical purposes is not recommended. For , the formula reads

(7.55)

which is equivalent to (7.51). For and, since also for , (7.52) reduces to

(7.56)