Preface to the Eighth Bdition Acknowledgments The Order of Presentation of the Formulas Use of the Tables Index of Special Functions Notation Note on the Bibliographic References 0 Introduction 0.1 Finite sums 0.11 Progressions 0.12 Sums of powers of natural numbers 0.13 Sums of reciprocals of natural numbers 0.14 Sums of products of reciprocals of natural numbers 0.15 Sums of the binomial coefficients 0.2 Numerical series and infinite products 0.21 The convergence of numerical series 0.22 Convergence tests 0.23-0.24 Examples of numerical series 0.25 Infinite products 0.26 Examples of infinite products 0.3 Functional series 0.30 Definitions and theorems 0.31 Power series 0.32 Fourier series 0.33 Asymptotic series 0.4 Certain formulas from diferential calculus 0.41 Differentiation of a definite integral with respect to a parameter 0.42 The nth derivative of a product (Leibniz's rule) 0.43 The nth derivative of a composite function 0.44 Integration by substitution 1 Elementary Functions 1.1 Power of Binomials 1.11 Power series 1.12 Series of rational fractions 1.2 The Exponential Function 1.21 Series representation 1.22 Functional relations 1.23 Series of exponentials 1.3-1.4 Trigonometric and Hyperbolic Functions 1.30 Introduction 1.31 The basic functional relations 1.32 The representation of powers of trigonometric and hyperbolic functionsin terms of functions of multiples of the argument (angle) 1.33 The representation of trigonometric and hyperbolic functions of multiples of the argument (angle) in terms of powers of these functions 1.34 Certain sums of trigonometric and hyperbolic functions 1.35 Sums of powers of trigonometric functions of multiple angles 1.36 Sums of products of trigonometric functions of multiple angles 1.37 Sums of tangents of multiple angles 1.38 Sums leading to hyperbolic tangents and cotangents 1.39 The representation of cosines and sines of multiples of the angle as finite products 1.41 The expansion of trigonometric and hyperbolic functions in power series
1.42 Expansion in series of simple fractions 1.43 Representation in the form of an infinite product 1.44-1.45 Trigonometric (Fourier) series 1.46 Series of products of exponential and trigonometric functions 1.47 Series of hyperbolic functions 1.48 Lobachevskiy's "Angle of parallelism" II (x) 1.49 The hyperbolic amplitude (the Gudermannian) gd x 1.5 The Logarithm 1.51 Series representation 1.52 Series of logarithms (cf.1.431) 1.6 The Inverse Trigonometric and Hyperbolic Functions 1.61 The domain of definition 1.62-1.63 Functional relations 1.64 Series representations 2 Indefinite Integrals of Elementary Functions 2.0 Introduction 2.00 General remarks 2.01 The basic integrals 2.02 General formulas 2.1 Rational Functions 2.10 General integration rules 2.11-2.13 Forms containing the binomial a+bxk 2.14 Forms containing the binomial 1+xn 2.15 Forms containing pairs of binomials: a +bx and α+βx 2.16 Forms containing the trinomial a+bxk+cx2k 2.17 Forms containing the quadratic trinomial a+bx+cx2 and powers of x 2.18 Forms containing the quadratic trinomial a+bx+cx2 and the binomial α+βr 2.2 Algebraic functions 2.20 Introduction 2.21 Forms containing the binomial a+bxk and □（數理化公式） …… 3-4 Definite Integrals of Elementary Functions 5 Indefinite Integrals of Special Functions 6-7 Definite Integrals of Special Functions 8-9 Special Functions 10 Vector Field Theory 11 Integral Inequalities 12 Fourier, Laplace, and Mellin Transforms References Supplemental references Index of Functions and Constants Index of Concepts
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