HP 40gs User Manual page 200

hp40g+.book Page 18 Friday, December 9, 2005 1:03 AM
IBP
14-18
and with period T (T being equal to the contents of the
variable PERIOD).
If f(x) is a discrete series, then:
2 iNxπ
∞
+
--------------- -
T
∑
f x ( )
= c e
N
∞
N = –
Example
Determine the Fourier coefficients of a periodic function f
with period 2π and defined over interval [0, 2π] by
2
f(x)=x .
Typing:
STORE(2π,PERIOD)
2
FOURIER(X ,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
2 i N π ⋅ ⋅ ⋅
+ 2
----------------------------------
2
N
≠
N 0
So if , then:
2 i N π ⋅ ⋅ ⋅
+ 2
----------------------------------
c =
N
2
N
Typing:
2
FOURIER(X ,0)
gives:
2
4 π ⋅
------------ -
3
N = 0
so if , then:
2
4 π ⋅
------------ -
c =
0
3
Partial integration
IBP has two parameters: an expression of the form
u x ( ) v' x ( ) ⋅ v x ( )
and .
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