Treatise of Physics

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theorem 17.3 Euler–Fourier coefficient formulas

open in the book · parts/02-mathematical-methods/15-fourier-integral-transforms.tex:135 · p. 672

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theorem 17.3: Euler–Fourier coefficient formulas17.3definition 17.1: Fourier coefficients and Fourier series17.1lemma 17.2: Orthogonality of the harmonics17.2proposition 28.47: Modal solution of the initial-value problem28.47proof : ch:15-fourier-integral-transforms@proof-2proofdefinition 17.25: Multiple Fourier series17.25lemma 17.6: Dirichlet kernel17.6lemma 17.15: A polynomial whose partial sum spikes at the origin17.15proposition 17.4: Least squares and Bessel's inequality17.4proposition 17.10: Smoothness and coefficient decay17.10proposition 17.86: The DFT is exact for a band-limited periodic signal17.86proposition 17.16: An explicit continuous function with a divergent Fourier series17.16theorem 17.47: Poisson summation17.47theorem 17.80: Sampling theorem17.80theorem 17.34: Parseval's identity for series17.34proof : ch:15-fourier-integral-transforms@proof-1proofequation 28.50: eq:osc-string-modes28.50proof : ch:11-oscillations-waves@proof-26proof

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typedirectionnode provenancewhere
depends_on → Fourier coefficients and Fourier series declared parts/02-mathematical-methods/15-fourier-integral-transforms.tex:142
depends_on → Orthogonality of the harmonics declared parts/02-mathematical-methods/15-fourier-integral-transforms.tex:142
depends_on ← Modal solution of the initial-value problem declared parts/03-classical-mechanics/11-oscillations-waves.tex:1684
proves ← ch:15-fourier-integral-transforms@proof-2 declared parts/02-mathematical-methods/15-fourier-integral-transforms.tex:145