Fourier Series; Function Fourier - HP 50g User Manual

Compare these expressions with the one given earlier in the definition of
the Laplace transform, i.e.,
and you will notice that the CAS default variable X in the equation writer
screen replaces the variable s in this definition. Therefore, when using the
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 e
-x
x e .

Fourier series

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

Function FOURIER

Function FOURIER provides the coefficient c
Fourier series given the function f(t) and the value of n.
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 ).
Page 14-5
) ( ( )
L f t F s
'1/(X+1)^2' ` ILAP
∑
f ) ( t c
n
2
i n
exp(
T
∫
) (
st
f t e dt
0
-X
', meaning that L
2 in t
exp( ),
n
T
) ,
t dt n
of the complex-form of the
n
,
-1 2
{1/(s+1) } =
,..., , 2 1 0 , 1 , 2 , ,...
The function
.