HP 50g manual Fourier series, Function Fourier, Lf t= F s = 0∞ f t ⋅ e− st dt, 2inπt

Compare these expressions with the one given earlier in the definition of the Laplace transform, i.e.,

L{f (t)}= F (s) = ∫0∞ f (t) ⋅ e− st dt,

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:

‘1/(X+1)^2’`ILAP

The calculator returns the result: ‘X⋅e-X’, meaning that L -1{1/(s+1)2} = x⋅e-x.

Fourier series

A complex Fourier series is defined by the following expression

					+∞		2inπt
				f (t) = ∑ cn ⋅ exp(				),
					n=−∞		T
where
cn	=	1	∫ T	f (t) ⋅ exp(	2 ⋅ i ⋅ n ⋅π	⋅ t) ⋅ dt,	n = −∞,...,−2,−1,0,1,2,...∞.
		T
			0		T

Function FOURIER

Function FOURIER provides the coefficient cn of the complex-form of the

Fourier 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).

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