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Table of integrals, series, and products / I. S. Gradshteyn and I. M. Ryzhik ; Daniel Zwillinger, Editor (Rensselaer Polytechnic Institute, USA)
Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: MyiLibraryPublisher: Amsterdam ; Heidelberg : Elsevier, Academic Press, [2015]Distributor: [LaVergne, Tenn.] : [MyiLibrary]Edition: Eighth editionDescription: 1 Online-Ressource (xlv, 1133 Seiten)ISBN:- 9781322158464
- 9780123849342
- 9780123849335
- 510.21
- 510.2/1 23
- 519
- QA55 .G6613 2014
Contents:
Summary: The Table of Integrals, Series, and Products is the essential reference for integrals in the English language. Mathematicians, scientists, and engineers, rely on it when identifying and subsequently solving extremely complex problems. Since publication of the first English-language edition in 1965, it has been thoroughly revised and enlarged on a regular basis, with substantial additions and, where necessary, existing entries corrected or revised. The seventh edition includes a fully searchable CD-Rom.- Fully searchable CD that puts information at your fingertips included with text- Most uPPN: PPN: 1653454288Package identifier: Produktsigel: ZDB-30-PAD | ZDB-30-PQE
Front Cover; Table of Integrals, Series, and Products; Copyright; Contents; Preface to the Eighth Edition; Acknowledgments; The Order of Presentation of the Formulas; Use of the Tables; Bernoulli and Euler Polynomials and Numbers; Elliptic Functions and Elliptic Integrals; The Jacobi Zeta Function and Theta Functions; Exponential and Related Integrals; Hermite and Chebyshev Orthogonal Polynomials; Bessel Functions; Parabolic Cylinder Functions and Whittaker Functions; Mathieu Functions; Index of Special Functions; Notation; Note on the Bibliographic References; 0 Introduction; 0.1 Finite sums
0.11 Progressions0.12 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 differential calculus
0.41 Differentiation of a definite integral with respect to a parameter0.42 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 functions in terms of functions of multiples of the argu ...1.33 The representation of trigonometric and hyperbolic functions of multiples of the argument (angle) in terms of powers...; 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 products1.41 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'' Π(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)
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