# 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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