HP 48gII 2inπt, Fourier series, Function FOURIER, f (t) = ∑ cn ⋅ exp, n = −∞,...,−2,−1,0,1,2,...∞, Fourier series for a quadratic function

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/EXP(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				T
			0

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).

Fourier series for a quadratic function

Determine the coefficients c0, c1, and c2 for the function g(t) = (t-1)2+(t-1), with period T = 2.

Using the calculator in ALG mode, first we define functions f(t) and g(t):

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