Fourier Series; Function Fourier; Fourier Series For A Quadratic Function - HP 48gII User Manual

and you will notice that the CAS default variable X in the equation writer
screen replaces the variable s in this definition.
function LAP you get back a function of X, which is the Laplace transform of
f(X).
Example 2 – Determine the inverse Laplace transform of F(s) = sin(s). Use:
The calculator returns the result: 'X/EXP(X)', meaning that L

Fourier series

A complex Fourier series is defined by the following expression
where
1
T
∫
= ⋅
c f ) ( t exp(
n
T
0

Function FOURIER

Function FOURIER provides the coefficient c
series given the function f(t) and the value of n. The function FOURIER
requires you to store the value of the period (T) of a T-periodic function into
the CAS variable PERIOD before calling the function. The function FOURIER is
available in the DERIV sub-menu within the CALC menu („Ö).

Fourier series for a quadratic function

Determine the coefficients c
period T = 2.
Using the calculator in ALG mode, first we define functions f(t) and g(t):
'1/(X+1)^2' ` ILAP
+∞
2 in
∑
= ⋅
f ) ( t c exp(
n
T
= −∞
n
π
⋅ ⋅ ⋅
2 i n
⋅ ⋅
t ) dt , n
T
of the complex-form of the Fourier
n
, c , and c for the function g(t) = (t-1)
0 1 2
Therefore, when using the
-1 2
{1/(s+1) } = x⋅e
π
t
),
= −∞ − −
,..., , 2 1 0 , 1 , 2 , ,...
2
+(t-1), with
Page 14-6
-x
.
∞
.