HP 40gs, User Manual

Page: 200 / 444

14-18 Computer Algebra System (CAS)
and with period T ( T being equal to the contents of the
variable PERIOD ).
If f(x) is a discrete series, then:
Example
Determine the Fourier coefficients of a periodic function f
with period 2
π
and defined over interval [0, 2
π
] by
f(x)=x
2
.
Typing:
STORE(2
π
,PERIOD)
FOURIER(X
2
,N)
The calculator does not know that N is a whole number,
so you have to replace EXP(2
∗
i
∗
N
∗π
) with 1 and then
simplify the expression. We get
So if , then:
Typing:
FOURIER(X
2
,0)
gives:
so if , then:
IBP
Partial integration
IBP has two parameters: an expression of the form
and .
f x
( )
c
N
e
2 iNx
π
T
----------------
N
∞
– =
∞
+
∑
=
2 i N
π
2 +
⋅ ⋅ ⋅
N
2
----------------------------------
N 0
≠
c
N
2 i N
π
2 +
⋅ ⋅ ⋅
N
2
----------------------------------
=
4
π
2
⋅
3
-------------
N 0 =
c
0
4
π
2
⋅
3
------------- =
u x
( )
v ' x
( ) ⋅
v x
( )
hp40g+.book Page 18 Friday, December 9, 2005 1:03 AM