HP 40gs User Manual
Page 200
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 2π and defined over interval [0, 2π] by
f(x)=x
2
.
Typing:
STORE(2π,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
2iNx
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