Table of integrals, series, and products

cover image

Where to find it

Kenan Science Library — Remote Storage

Call Number
QA55 .G6613 1994
Status
Available

Summary

This volume, which contains nearly 20,000 formulae for integrals, sums, series, products and special functions, is a reference source for integrals in the English language. Mathematicians, scientists and engineers can use it when identifying and solving extremely complex problems.

Contents

  • Preface to the Sixth Edition p. xxi
  • Acknowledgments p. xxiii
  • The order of presentation of the formulas p. xxvii
  • Use of the tables p. xxxi
  • Special functions p. xxxix
  • Notation p. xliii
  • Note on the bibliographic references p. xlvii
  • 0 Introduction p. 1
  • 0.1 Finite sums p. 1
  • 0.2 Numerical series and infinite products p. 6
  • 0.3 Functional series p. 15
  • 0.4 Certain formulas from differential calculus p. 21
  • 1 Elementary Functions p. 25
  • 1.1 Power of Binomials p. 25
  • 1.2 The Exponential Function p. 26
  • 1.3-1.4 Trigonometric and Hyperbolic Functions p. 27
  • 1.5 The Logarithm p. 51
  • 1.6 The Inverse Trigonometric and Hyperbolic Functions p. 54
  • 2 Indefinite Integrals of Elementary Functions p. 61
  • 2.0 Introduction p. 61
  • 2.1 Rational functions p. 64
  • 2.2 Algebraic functions p. 80
  • 2.3 The Exponential Function p. 104
  • 2.4 Hyperbolic Functions p. 105
  • 2.5-2.6 Trigonometric Functions p. 147
  • 2.7 Logarithms and Inverse-Hyperbolic Functions p. 233
  • 2.8 Inverse Trigonometric Functions p. 237
  • 3-4 Definite Integrals of Elementary Functions p. 243
  • 3.0 Introduction p. 243
  • 3.1-3.2 Power and Algebraic Functions p. 248
  • 3.3-3.4 Exponential Functions p. 331
  • 3.5 Hyperbolic Functions p. 365
  • 3.6-4.1 Trigonometric Functions p. 384
  • 4.2-4.4 Logarithmic Functions p. 522
  • 4.5 Inverse Trigonometric Functions p. 596
  • 4.6 Multiple Integrals p. 604
  • 5 Indefinite Integrals of Special Functions p. 615
  • 5.1 Elliptic Integrals and Functions p. 615
  • 5.2 The Exponential Integral Function p. 622
  • 5.3 The Sine Integral and the Cosine Integral p. 623
  • 5.4 The Probability Integral and Fresnel Integrals p. 623
  • 5.5 Bessel Functions p. 624
  • 6-7 Definite Integrals of Special Functions p. 625
  • 6.1 Elliptic Integrals and Functions p. 625
  • 6.2-6.3 The Exponential Integral Function and Functions Generated by It p. 630
  • 6.4 The Gamma Function and Functions Generated by It p. 644
  • 6.5-6.7 Bessel Functions p. 652
  • 6.8 Functions Generated by Bessel Functions p. 745
  • 6.9 Mathieu Functions p. 755
  • 7.1-7.2 Associated Legendre Functions p. 762
  • 7.3-7.4 Orthogonal Polynomials p. 788
  • 7.5 Hypergeometric Functions p. 806
  • 7.6 Confluent Hypergeometric Functions p. 814
  • 7.7 Parabolic Cylinder Functions p. 835
  • 7.8 Meijer's and MacRobert's Functions (G and E) p. 843
  • 8-9 Special Functions p. 851
  • 8.1 Elliptic integrals and functions p. 851
  • 8.2 The Exponential Integral Function and Functions Generated by It p. 875
  • 8.3 Euler's Integrals of the First and Second Kinds p. 883
  • 8.4-8.5 Bessel Functions and Functions Associated with Them p. 900
  • 8.6 Mathieu Functions p. 940
  • 8.7-8.8 Associated Legendre Functions p. 948
  • 8.9 Orthogonal Polynomials p. 972
  • 9.1 Hypergeometric Functions p. 995
  • 9.2 Confluent Hypergeometric Functions p. 1012
  • 9.3 Meijer's G-Function p. 1022
  • 9.4 MacRobert's E-Function p. 1025
  • 9.5 Riemann's Zeta Functions [zeta] (z, q), and [zeta] (z), and the Functions [Phi] (z, s, v) and [xi] (s) p. 1026
  • 9.6 Bernoulli numbers and polynomials, Euler numbers p. 1030
  • 9.7 Constants p. 1035
  • 10 Vector Field Theory p. 1039
  • 10.1-10.8 Vectors, Vector Operators, and Integral Theorems p. 1039
  • 11 Algebraic Inequalities p. 1049
  • 11.1-11.3 General Algebraic Inequalities p. 1049
  • 12 Integral Inequalities p. 1053
  • 12.11 Mean value theorems p. 1053
  • 12.21 Differentiation of definite integral containing a parameter p. 1054
  • 12.31 Integral inequalities p. 1054
  • 12.41 Convexity and Jensen's inequality p. 1056
  • 12.51 Fourier series and related inequalities p. 1056
  • 13 Matrices and related results p. 1059
  • 13.11-13.12 Special matrices p. 1059
  • 13.21 Quadratic forms p. 1061
  • 13.31 Differentiation of matrices p. 1063
  • 13.41 The matrix exponential p. 1064
  • 14 Determinants p. 1065
  • 14.11 Expansion of second- and third-order determinants p. 1065
  • 14.12 Basic properties p. 1065
  • 14.13 Minors and cofactors of a determinant p. 1065
  • 14.14 Principal minors p. 1066
  • 14.15 Laplace expansion of a determinant p. 1066
  • 14.16 Jacobi's theorem p. 1066
  • 14.17 Hadamard's theorem p. 1066
  • 14.18 Hadamard's inequality p. 1067
  • 14.21 Cramer's rule p. 1067
  • 14.31 Some special determinants p. 1068
  • 15 Norms p. 1071
  • 15.1-15.9 Vector Norms p. 1071
  • 15.11 General properties p. 1071
  • 15.21 Principal vector norms p. 1071
  • 15.31 Matrix norms p. 1072
  • 15.41 Principal natural norms p. 1072
  • 15.51 Spectral radius of a square matrix p. 1073
  • 15.61 Inequalities involving eigenvalues of matrices p. 1074
  • 15.71 Inequalities for the characteristic polynomial p. 1074
  • 15.81-15.82 Named theorems on eigenvalues p. 1076
  • 15.91 Variational principles p. 1081
  • 16 Ordinary differential equations p. 1083
  • 16.1-16.9 Results relating to the solution of ordinary differential equations p. 1083
  • 16.11 First-order equations p. 1083
  • 16.21 Fundamental inequalities and related results p. 1084
  • 16.31 First-order systems p. 1085
  • 16.41 Some special types of elementary differential equations p. 1087
  • 16.51 Second-order equations p. 1088
  • 16.61-16.62 Oscillation and non-oscillation theorems for second-order equations p. 1090
  • 16.71 Two related comparison theorems p. 1093
  • 16.81-16.82 Non-oscillatory solutions p. 1093
  • 16.91 Some growth estimates for solutions of second-order equations p. 1094
  • 16.92 Boundedness theorems p. 1096
  • 17 Fourier, Laplace, and Mellin Transforms p. 1099
  • 17.1-17.4 Integral Transforms p. 1099
  • 18 The z-transform p. 1127
  • 18.1-18.3 Definition, Bilateral, and Unilateral z-Transforms p. 1127
  • References p. 1133
  • Supplemental references p. 1137
  • Function and constant index p. 1143
  • General index p. 1153

Subjects

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