HP F2226A - 48GII Graphic Calculator User Manual page 509

A general expression for c
The function FOURIER can provide a general expression for the coefficient c
of the complex Fourier series expansion.
function g(t) as before, the general term c
font and small font displays):
The general expression turns out to be, after simplifying the previous result,
( n
c =
n
We can simplify this expression even further by using Euler's formula for
complex numbers, namely, e
cos(2nπ) = 1, and sin(2nπ) = 0, for n integer.
Using the calculator you can simplify the expression in the equation writer
(‚O) by replacing e
simplification:
The result is
Putting together the complex Fourier series
Having determined the general expression for c
complex Fourier series by using the summation function (Σ) in the calculator as
follows:
n
For example, using the same
is given by (figures show normal
n
2 in π 2 2
π + 2 i ) ⋅ e + 2 i n π
3 3 2 in π
2 n π ⋅ e
π
2in
= cos(2nπ) + i⋅sin(2nπ) = 1 + i⋅0 = 1, since
π
2in
= 1. The figure shows the expression after
2 ⋅π 2
c = (i⋅n⋅π+2)/(n
n
2
+ 3 n π − 2 i
).
, we can put together a finite
n
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n