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**Table of integrals, series, and products. Transl. from the Russian by Scripta Technica, Inc.
5th ed.**
*(English)*
Zbl 0918.65002

Boston, MA: Academic Press, Inc. xlvii, 1204 p. (1994).

Publisher’s description: This handbook is the Fifth Edition of one of Academic Press’s all-time best-sellers. The volume, which contains nearly 20,000 formulae for integrals, sums, series, products, and special functions, is the major reference source for integrals in the English language. It is an essential reference for mathematicians, scientists, and engineers, who rely on it when identifying and subsequently solving extremely complex problems.

Contents: Introduction. Elementary Functions. Indefinite Integrals of Elementary Functions. Definite Integrals of Elementary Functions. Indefinite Integrals of Special Functions. Definite Integrals of Special Functions. Special Functions. Vector Field Theory. Algebraic Inequalities. Integral Inequalities. Matrices and Related Results. Determinants. Norms. Ordinary Differential Equations. Fourier, Laplace and Mellin Transforms. Bibliographic References. Classified Supplementary References.

Contents: Introduction. Elementary Functions. Indefinite Integrals of Elementary Functions. Definite Integrals of Elementary Functions. Indefinite Integrals of Special Functions. Definite Integrals of Special Functions. Special Functions. Vector Field Theory. Algebraic Inequalities. Integral Inequalities. Matrices and Related Results. Determinants. Norms. Ordinary Differential Equations. Fourier, Laplace and Mellin Transforms. Bibliographic References. Classified Supplementary References.

### MSC:

65A05 | Tables in numerical analysis |

00A22 | Formularies |

33-00 | General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to special functions |

40-00 | General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to sequences, series, summability |

### Citations:

Zbl 0456.65001; Zbl 0448.65002; Zbl 0521.33001; Zbl 0103.03801; Zbl 0080.33703; Zbl 0044.13303; Zbl 0918.65001
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\textit{I. S. Gradshteyn} and \textit{I. M. Ryzhik}, Table of integrals, series, and products. Transl. from the Russian by Scripta Technica, Inc. 5th ed. Boston, MA: Academic Press, Inc. (1994; Zbl 0918.65002)

### Online Encyclopedia of Integer Sequences:

Bessel polynomials y_n(x) (see A001498) evaluated at 2.Coefficients of Chebyshev polynomials of the first kind: triangle of coefficients in expansion of cos(n*x) in descending powers of cos(x).

Triangle of coefficients in expansion of sin(n*x) (or sin(n*x)/cos(x) if n is even) in ascending powers of sin(x).

a(n) = 2^n*Sum_{k=0..n} (n+k)!/((n-k)!*k!*4^k).

Triangle giving coefficients of (n+1)!*B_n(x), where B_n(x) is a Bernoulli polynomial. Rising powers of x.

Triangle giving coefficients of (n+1)!*B_n(x), where B_n(x) is a Bernoulli polynomial, ordered by falling powers of x.