HP 48gII Graphing Calculator Manual do Utilizador descarregar pdf (Página 509)

A general expression for c

The function FOURIER can provide a general expression for the coefficient c

of the complex Fourier series expansion. For example, using the same

function g(t) as before, the general term c

is given by (figures show normal

font and small font displays):

The general expression turns out to be, after simplifying the previous result,

We can simplify this expression even further by using Euler’s formula for

complex numbers, namely, e

= cos(2nπ) + i⋅sin(2nπ) = 1 + i⋅0 = 1, since

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

= 1. The figure shows the expression after

simplification:

The result is c

= (i⋅n⋅π+2)/(n

Putting together the complex Fourier series

Having determined the general expression for c

, we can put together a finite

complex Fourier series by using the summation function (Σ) in the calculator as

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HP 48gII Graphing Calculator Manual do Utilizador Página 509