HP 50g HP 50g_user's manual_English_HDPSG49AEM8.pdf - Page 148

Compare these expressions with the one given earlier in the definition of the Laplace transform, i.e., ∫ L{f (t)}= F (s) = ∞ f (t) ⋅ e−stdt, 0 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 ∑ f (t) = +∞ n=−∞ cn ⋅ exp( 2inπt T ), where ∫ cn = 1 T T f (t) ⋅ exp( 2 ⋅ i ⋅ n ⋅π ⋅ t) ⋅ dt, 0 T n 2,−1,0,1,2,...∞. 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). Page 14-5