# Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 20

## Murray R. Spiegel: Mathematical Handbook of Formulas and Tables: Chapter 20

Published $1968$.

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## $20 \quad$ Taylor Series

### Taylor Series for Functions of One Variable

$20.1$: Taylor Series: Remainder
$20.2$: Taylor Series: Remainder: Lagrange Form
$20.3$: Taylor Series: Remainder: Cauchy Form
Taylor Series
Maclaurin Series
Interval of Convergence

### Binomial Series

$20.4$: Binomial Theorem: General Binomial Theorem
$20.5$: Square of Sum: Algebraic Proof 2
$20.6$: Binomial Theorem: Examples: Cube of Sum
$20.7$: Binomial Theorem: Examples: 4th Power of Sum
$20.8$: Power Series Expansion of $\dfrac 1 {1 + x}$: Proof 2
$20.9$: Power Series Expansion of $\dfrac 1 {\paren {1 + x}^2}$: Proof 2
$20.10$: Power Series Expansion of $\dfrac 1 {\paren {1 + x}^3}$: Proof 2
$20.11$: Power Series Expansion of $\dfrac 1 {\sqrt {1 + x} }$
$20.12$: Power Series Expansion of $\sqrt {1 + x}$
$20.13$: Power Series Expansion of $\dfrac 1 {\sqrt  {1 + x} }$
$20.14$: Power Series Expansion of $\sqrt  {1 + x}$

### Series for Exponential and Logarithmic Functions

$20.15$: Power Series Expansion for Exponential Function
$20.16$: Power Series Expansion for General Exponential Function
$20.17$: Power Series Expansion for $\map \ln {1 + x}$
$20.18$: Power Series Expansion for $\dfrac 1 2 \map \ln {\dfrac {1 + x} {1 - x} }$
$20.19$: Power Series Expansion for $\ln x$: Formulation 1
$20.20$: Power Series Expansion for $\ln x$: Formulation 2

### Series for Trigonometric Functions

$20.21$: Power Series Expansion for Sine Function
$20.22$: Power Series Expansion for Cosine Function
$20.23$: Power Series Expansion for Tangent Function
$20.24$: Power Series Expansion for Cotangent Function
$20.25$: Power Series Expansion for Secant Function
$20.26$: Power Series Expansion for Cosecant Function
$20.27$: Power Series Expansion for Real Arcsine Function
$20.28$: Power Series Expansion for Real Arccosine Function
$20.29$: Power Series Expansion for Real Arctangent Function
$20.30$: Power Series Expansion for Real Arccotangent Function
$20.31$: Power Series Expansion for Real Arcsecant Function
$20.32$: Power Series Expansion for Real Arccosecant Function

### Series for Hyperbolic Functions

$20.33$: Power Series Expansion for Hyperbolic Sine Function
$20.34$: Power Series Expansion for Hyperbolic Cosine Function
$20.35$: Power Series Expansion for Hyperbolic Tangent Function
$20.36$: Power Series Expansion for Hyperbolic Cotangent Function
$20.37$: Power Series Expansion for Hyperbolic Secant Function
$20.38$: Power Series Expansion for Hyperbolic Cosecant Function
$20.39$: Power Series Expansion for Real Inverse Hyperbolic Sine
$20.40$: Power Series Expansion for Real Inverse Hyperbolic Cosine
$20.41$: Power Series Expansion for Real Inverse Hyperbolic Tangent
$20.42$: Power Series Expansion for Real Inverse Hyperbolic Cotangent

### Miscllaneous Series

$20.43$: Power Series Expansion for $e^{\sin x}$
$20.44$: Power Series Expansion for $e^{\cos x}$
$20.45$: Power Series Expansion for $e^{\tan x}$
$20.46$: Power Series Expansion for $e^x \sin x$
$20.47$: Power Series Expansion for $e^x \cos x$
$20.48$: Power Series Expansion for $\ln \size {\sin x}$
$20.49$: Power Series Expansion for $\ln \size {\cos x}$
$20.50$: Power Series Expansion for $\ln \size {\tan x}$
$20.51$: Power Series Expansion for $\dfrac {\map \ln {1 + x} } {1 + x}$

### Reversion of Power Series

$20.52 - 59$: Reversion of Power Series

### Taylor Series for Functions of Two Variables

$20.60$: Taylor Series: Two Variables

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