HP 40gs hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 200
Partial integration
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hp40g+.book Page 18 Friday, December 9, 2005 1:03 AM IBP 14-18 and with period T (T being equal to the contents of the variable PERIOD). If f(x) is a discrete series, then: f(x) = +∞ 2----i--N-----x---π- ∑ cNe T N = -∞ Example Determine the Fourier coefficients of a periodic function f with period 2π and defined over interval [0, 2π] by f(x)=x2. Typing: STORE(2π,PERIOD) FOURIER(X2,N) The calculator does not know that N is a whole number, so you have to replace EXP(2∗ i∗N∗π) with 1 and then simplify the expression. We get 2-----⋅---i---⋅---N 2-N2 So if N ≠ 0 , then: cN = 2-----⋅---i---⋅---N 2-N2 Typing: FOURIER(X2,0) gives: -4 23 so if N = 0 , then: c0 = -4 2 3 Partial integration IBP has two parameters: an expression of the form u(x) ⋅ v'(x) and v(x) . Computer Algebra System (CAS)