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

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

Published $\text {1968}$

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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

$20.4$: 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 for $\dfrac 1 {1 + x}$: Proof 2

$20.9$: Power Series Expansion for $\dfrac 1 {\paren {1 + x}^2}$: Proof 2

$20.10$: Power Series Expansion for $\dfrac 1 {\paren {1 + x}^3}$: Proof 2

$20.11$: Power Series Expansion for $\dfrac 1 {\sqrt {1 + x} }$

$20.12$: Power Series Expansion for $\sqrt {1 + x}$

$20.13$: Power Series Expansion for $\dfrac 1 {\sqrt [3] {1 + x} }$

$20.14$: Power Series Expansion for $\sqrt [3] {1 + x}$

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 Area Hyperbolic Sine

$20.40$: Power Series Expansion for Real Area Hyperbolic Cosine

$20.41$: Power Series Expansion for Real Area Hyperbolic Tangent

$20.42$: Power Series Expansion for Real Area 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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