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| Preface | |
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| Preface to the Second Edition | |
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| Index of Special Functions and Notations | |
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| Quick Reference List of Frequently Used Data | |
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| Useful Identities | |
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| Complex Relationships | |
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| Constants | |
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| Derivatives of Elementary Functions | |
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| Rules of Differentiation and Integration | |
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| Standard Integrals | |
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| Standard Series | |
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| Geometry | |
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| Numerical, Algebraic, and Analytical Results for Series and Calculus | |
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| Algebraic Results Involving Real and Complex Numbers | |
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| Finite Sums | |
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| Bernoulli and Euler Numbers and Polynomials | |
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| Determinants | |
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| Matrices | |
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| Permutations and Combinations | |
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| Partial Fraction Decomposition | |
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| Convergence of Series | |
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| Infinite Products | |
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| Functional Series | |
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| Power Series | |
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| Taylor Series | |
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| Fourier Series | |
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| Asymptotic Expansions | |
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| Basic Results from the Calculus | |
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| Functions and Identities | |
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| Complex Numbers and Trigonometric and Hyperbolic Functions | |
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| Logarithms and Exponentials | |
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| The Exponential Function | |
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| Trigonometric Identities | |
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| Hyperbolic Identities | |
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| The Logarithm | |
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| Inverse Trigonometric and Hyperbolic Functions | |
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| Series Representations of Trigonometric and Hyperbolic Functions | |
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| Useful Limiting Values and Inequalities Involving Elementary Functions | |
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| Derivatives of Elementary Functions | |
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| Derivatives of Algebraic, Logarithmic, and Exponential Functions | |
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| Derivatives of Trigonometric Functions | |
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| Derivatives of Inverse Trigonometric Functions | |
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| Derivatives of Hyperbolic Functions | |
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| Derivatives of Inverse Hyperbolic Functions | |
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| Indefinite Integrals of Algebraic Functions | |
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| Algebraic and Transcendental Functions | |
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| Indefinite Integrals of Rational Functions | |
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| Nonrational Algebraic Functions | |
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| Indefinite Integrals of Exponential Functions | |
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| Basic Results | |
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| Indefinite Integrals of Logarithmic Functions | |
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| Combinations of Logarithms and Polynomials | |
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| Indefinite Integrals of Hyperbolic Functions | |
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| Basic Results | |
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| Integrands Involving Powers of sinh(bx) or cosh(bx) | |
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| Integrands Involving (a [plus or minus] bx)[superscript m] sinh(cx) or (a + bx)[superscript m] cosh(cx) | |
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| Integrands Involving x[superscript m] sinh[superscript n] x or x[superscript m] cosh[superscript n] x | |
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| Integrands Involving x[superscript m] sinh[superscript -n] x or x[superscript m] cosh[superscript -n] x | |
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| Integrands Involving (1 [plus or minus] cosh x)[superscript -m] | |
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| Integrands Involving sinh(ax)cosh[superscript -n] x or cosh(ax)sinh[superscript -n] x | |
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| Integrands Involving sinh(ax + b) and cosh(cx + d) | |
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| Integrands Involving tanh kx and coth kx | |
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| Integrands Involving (a + bx)[superscript m] sinh kx or (a + bx)[superscript m] cosh kx | |
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| Indefinite Integrals Involving Inverse Hyperbolic Functions | |
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| Basic Results | |
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| Integrands Involving x[superscript -n] arcsinh(x/a) or x[superscript -n] arccosh(x/a) | |
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| Integrands Involving x[superscript n] arctanh(x/a) or x[superscript n] arccoth(x/a) | |
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| Integrands Involving x[superscript -n] arctanh(x/a) or x[superscript -n] arccoth(x/a) | |
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| Indefinite Integrals of Trigonometric Functions | |
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| Basic Results | |
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| Integrands Involving Powers of x and Powers of sin x or cos x | |
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| Integrands Involving tan x and/or cot x | |
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| Integrands Involving sin x and cos x | |
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| Integrands Involving Sines and Cosines with Linear Arguments and Powers of x | |
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| Indefinite Integrals of Inverse Trigonometric Functions | |
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| Integrands Involving Powers of x and Powers of Inverse Trigonometric Functions | |
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| The Gamma, Beta, Pi, and Psi Functions | |
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| The Euler Integral and Limit and Infinite Product Representations for [Gamma] (x) | |
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| Elliptic Integrals and Functions | |
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| Elliptic Integrals | |
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| Jacobian Elliptic Functions | |
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| Derivatives and Integrals | |
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| Inverse Jacobian Elliptic Functions | |
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| Probability Integrals and the Error Function | |
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| Normal Distribution | |
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| The Error Function | |
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| Fresnel Integrals, Sine and Cosine Integrals | |
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| Definitions, Series Representations, and Values at Intinity | |
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| Definitions, Series Representations, and Values at Infinity | |
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| Definite Integrals | |
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| Integrands Involving Powers of x | |
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| Integrands Involving Trigonometric Functions | |
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| Integrands Involving the Exponential Function | |
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| Integrands Involving the Hyperbolic Function | |
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| Integrands Involving the Logarithmic Function | |
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| Different Forms of Fourier Series | |
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| Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] | |
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| Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L | |
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| Fourier Series for f(x) on a [less than or equal] x [less than or equal] b | |
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| Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] | |
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| Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] L | |
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| Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] | |
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| Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] L | |
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| Complex (Exponential) Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] | |
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| Complex (Exponential) Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L | |
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| Representative Examples of Fourier Series | |
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| Fourier Series and Discontinuous Functions | |
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| Bessel Functions | |
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| Bessel's Differential Equation | |
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| Series Expansions for J[subscript v](x) and Y[subscript v](x) | |
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| Bessel Functions of Fractional Order | |
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| Asymptotic Representations for Bessel Functions | |
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| Zeros of Bessel Functions | |
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| Bessel's Modified Equation | |
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| Series Expansions for I[subscript v](x) and K[subscript v](x) | |
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| Modified Bessel Functions of Fractional Order | |
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| Asymptotic Representations of Modified Bessel Functions | |
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| Relationships between Bessel Functions | |
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| Integral Representations of J[subscript n](x), I[subscript n](x), and K[subscript n](x) | |
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| Indefinite Integrals of Bessel Functions | |
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| Definite Integrals Involving Bessel Functions | |
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| Spherical Bessel Functions | |
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| Orthogonal Polynomials | |
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| Introduction | |
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| Legendre Polynomials P[subscript n](x) | |
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| Chebyshev Polynomials T[subscript n](x) and U[subscript n](x) | |
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| Laguerre Polynomials L[subscript n](x) | |
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| Hermite Polynomials H[subscript n](x) | |
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| Laplace Transformation | |
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| Introduction | |
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| Fourier Transforms | |
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| Introduction | |
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| Numerical Integration | |
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| Classical Methods | |
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| Solutions of Standard Ordinary Differential Equations | |
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| Introduction | |
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| Separation of Variables | |
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| Linear First-Order Equations | |
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| Bernoulli's Equation | |
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| Exact Equations | |
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| Homogeneous Equations | |
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| Linear Differential Equations | |
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| Constant Coefficient Linear Differential Equations--Homogeneous Case | |
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| Linear Homogeneous Second-Order Equation | |
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| Constant Coefficient Linear Differential Equations--Inhomogeneous Case | |
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| Linear Inhomogeneous Second-Order Equation | |
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| Determination of Particular Integrals by the Method of Undetermined Coefficients | |
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| The Cauchy-Euler Equation | |
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| Legendre's Equation | |
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| Bessel's Equations | |
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| Power Series and Frobenius Methods | |
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| The Hypergeometric Equation | |
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| Numerical Methods | |
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| Vector Analysis | |
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| Scalars and Vectors | |
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| Scalar Products | |
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| Vector Products | |
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| Triple Products | |
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| Products of Four Vectors | |
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| Derivatives of Vector Functions of a Scalar t | |
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| Derivatives of Vector Functions of Several Scalar Variables | |
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| Integrals of Vector Functions of a Scalar Variable t | |
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| Line Integrals | |
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| Vector Integral Theorems | |
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| A Vector Rate of Change Theorem | |
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| Useful Vector Identities and Results | |
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| Systems of Orthogonal Coordinates | |
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| Curvilinear Coordinates | |
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| Vector Operators in Orthogonal Coordinates | |
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| Systems of Orthogonal Coordinates | |
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| Partial Differential Equations and Special Functions | |
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| Fundamental Ideas | |
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| Method of Separation of Variables | |
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| The Sturm-Liouville Problem and Special Functions | |
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| A First-Order System and the Wave Equation | |
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| Conservation Equations (Laws) | |
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| The Method of Characteristics | |
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| Discontinuous Solutions (Shocks) | |
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| Similarity Solutions | |
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| Burgers's Equation, the KdV Equation, and the KdVB Equation | |
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| The z-Transform | |
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| The z-Transform and Transform Pairs | |
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| Numerical Approximation | |
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| Introduction | |
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| Economization of Series | |
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| Pade Approximation | |
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| Finite Difference Approximations to Ordinary and Partial Derivatives | |
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| Short Classified Reference List | |
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| Index | |