HP 48gII - Manual (Page 511)

Page 16-33
The function
@@@F@@@ can be used to generate the expression for the complex
Fourier series for a finite value of k. For example, for k = 2, c
0
= 1/3,and
using t as the independent variable, we can evaluate F(t,2,1/3) to get:
This result shows only the first term (c0) and part of the first exponential term
in the series. The decimal display format was changed to Fix with 2 decimals
to be able to show some of the coefficients in the expansion and in the
exponent. As expected, the coefficients are complex numbers.
The function F, thus defined, is fine for obtaining values of the finite Fourier
series. For example, a single value of the series, e.g., F(0.5,2,1/3), can be
obtained by using (CAS modes set to Exact, step-by-step, and Complex):
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.)