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16. Use the De Moivre formulas (11) to derive the standard formulas for cos (0 + 6) and sin (0 + ø). THE COMPLEX FORM OF THE FULL FOURIER SERIES The eigenfunctions of -d²/dx² on (-1, 1) with the periodic boundary conditions are sin(nлx/l) and cos(nëx/l). But recall the DeMoivre formulas, which express the sine and cosine in terms of the complex exponentials: eie -i0 - e ei te -i0 sin 0 and cos 0: = 2i 2 (11)

16. Use the De Moivre formulas (11) to derive the standard formulas for cos (0 + 6) and sin (0 + ø). THE COMPLEX FORM OF THE FULL FOURIER SERIES The eigenfunctions of -d²/dx² on (-1, 1) with the periodic boundary conditions are sin(nлx/l) and cos(nëx/l). But recall the DeMoivre formulas, which express the sine and cosine in terms of the complex exponentials: eie -i0 - e ei te -i0 sin 0 and cos 0: = 2i 2 (11)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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16. Use the De Moivre formulas (11) to derive the standard formulas for cos (0 + 6) and sin (0 + ø).
Transcribed Image Text:16. Use the De Moivre formulas (11) to derive the standard formulas for cos (0 + 6) and sin (0 + ø).
THE COMPLEX FORM OF THE FULL FOURIER SERIES The eigenfunctions of -d²/dx² on (-1, 1) with the periodic boundary conditions are sin(nлx/l) and cos(nëx/l). But recall the DeMoivre formulas, which express the sine and cosine in terms of the complex exponentials: eie -i0 - e ei te -i0 sin 0 and cos 0: = 2i 2 (11)
Transcribed Image Text:THE COMPLEX FORM OF THE FULL FOURIER SERIES The eigenfunctions of -d²/dx² on (-1, 1) with the periodic boundary conditions are sin(nлx/l) and cos(nëx/l). But recall the DeMoivre formulas, which express the sine and cosine in terms of the complex exponentials: eie -i0 - e ei te -i0 sin 0 and cos 0: = 2i 2 (11)
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