Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 23

Murray R. Spiegel: Mathematical Handbook of Formulas and Tables: Chapter 23

Published $\text {1968}$

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$23 \quad$ Fourier Series

Definition of a Fourier Series

$23.1$, $23.2$: Fourier Series

Complex Form of Fourier Series

$23.3$, $23.4$: Fourier Series: Complex Form

Parseval's Identity

$23.5$: Parseval's Identity

Generalized Parseval Identity

$23.6$: Generalized Parseval's Identity

Special Fourier Series and their Graphs

$23.7$: Square Wave

$23.8$: Triangle Wave

$23.9$: Sawtooth Wave

$23.10$: Fourier Series/Half Sawtooth Wave

$23.11$: Fourier Series/Full Rectified Sine Wave

$23.12$: Fourier Series/Half Rectified Sine Wave

$23.13$: Half-Range Fourier Sine Series for Cosine over $0$ to $\pi$

$23.14$: Fourier Series/x squared over $-\pi$ to $\pi$

$23.15$: Half-Range Fourier Cosine Series for $x \paren {\pi - x}$ over $0$ to $\pi$

$23.16$: x by Pi minus x by Pi plus x over Minus Pi to Pi

$23.17$: 1 over Pi minus Alpha to Pi plus Alpha about Pi

$23.18$: Half-Range Fourier Sine Series for $x \paren {\pi - x}$ over $0$ to $\pi$

Miscellaneous Fourier Series

$23.19$: Sine of Non-Integer Multiple of $x$ over $0$ to $\pi$

$23.20$: Cosine of Non-Integer Multiple of $x$ over $0$ to $\pi$

$23.21$: Arctangent of a sin x over 1 minus a cos x

$23.22$: Log of 1 - 2 a cos x + a squared

$23.23$: Half Arctangent of 2 a sin x over 1 minus a squared

$23.24$: Half Arctangent of 2 a cos x over 1 minus a squared

$23.25$: e to Multiple of x

$23.26$: Hyperbolic Sine of Multiple of x

$23.27$: Hyperbolic Cosine of Multiple of x

$23.28$: Log of Sine of Half x

$23.29$: Log of Cosine of Half x

$23.30$: Pi Squared over 6 - Half Pi x + x squared over 4

$23.31$: 12 x by x - pi by x - 2 pi

$23.32$: Pi to the 4 over 90 - pi squared x squared over 12 + pi x cubed over 12 - x to the 4 over 48

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