HP 50g Graphing Calculator User Manual

Page 510

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Page 16-33

Accept change to

Approx

mode if requested. The result is the value

–0.40467…. The actual value of the function g(0.5) is g(0.5) = -0.25. The
following calculations show how well the Fourier series approximates this value
as the number of components in the series, given by k, increases:

F (0.5, 1, 1/3) = (-0.303286439037,0.)
F (0.5, 2, 1/3) = (-0.404607622676,0.)
F (0.5, 3, 1/3) = (-0.192401031886,0.)
F (0.5, 4, 1/3) = (-0.167070735979,0.)
F (0.5, 5, 1/3) = (-0.294394690453,0.)
F (0.5, 6, 1/3) = (-0.305652599743,0.)

To compare the results from the series with those of the original function, load
these functions into the PLOT – FUNCTION input form (

„ñ, simultaneously

if using RPN mode):

Change the limits of the Plot Window (

„ò) as follows:

Press the soft-menu keys

@ERASE @DRAW to produce the plot:

Notice that the series, with 5 terms, “hugs” the graph of the function very closely
in the interval 0 to 2 (i.e., through the period T = 2). You can also notice a

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