HP 50g Graphing Calculator - Manual (Page 508)

Page 16-31
The result is c
n
= (i ⋅n⋅π+2)/(n 2 ⋅π 2 ).
Putting together the complex Fourier series
Having determined the general expression for c
n
, we can put together a finite
complex Fourier series by using the summation function ( Σ) in the calculator as
follows:
Θ First, define a function c(n) representing the general term c
n
in the complex
Fourier series.
Θ Next, define the finite complex Fourier series, F(X,k), where X is the
independent variable and k determines the number of terms to be used.
Ideally we would like to write this finite complex Fourier series as
However, because the function c(n) is not defined for n = 0, we will be
better advised to re-write the expression as
)
2
exp( ) ( ) , ( X
T
n i
n c k X F
k
k n
⋅
⋅ ⋅ ⋅
⋅ =
∑
− =
π
+ = 0 ) 0 , , ( c c k X F
)],
2
exp( ) ( )
2
exp( ) ( [
1
X
T
n i
n c X
T
n i
n c
k
n
⋅
⋅ ⋅ ⋅
− ⋅ − + ⋅
⋅ ⋅ ⋅
⋅
∑
=
π π