HP 49g manual Function FOURIER`, Fourier series for a quadratic function, Where

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A complex Fourier

Fourier series

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

Function FOURIER`

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

series is defined by the following expression

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

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 (					).
Fourier series for a quadratic function				„Ö
Determine the coefficients c , c , and c			for the function g(t)		= (t-1)2+(t-1), with
period T = 2.∫	0 1 ∑	2