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

Graphing calculator.

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

### 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
.
.  