# Handbook of Mathematical Formulas and Integrals

**By**

- Alan Jeffrey, University at Newcastle Upon Tyne, UK
- Hui Dai, City University of Hong Kong, Kowloon, HK

The extensive additions, and the inclusion of a new chapter, has made this classic work by Jeffrey, now joined by co-author Dr. H.H. Dai, an even more essential reference for researchers and students in applied mathematics, engineering, and physics. It provides quick access to important formulas, relationships between functions, and mathematical techniques that range from matrix theory and integrals of commonly occurring functions to vector calculus, ordinary and partial differential equations, special functions, Fourier series, orthogonal polynomials, and Laplace and Fourier transforms. During the preparation of this edition full advantage was taken of the recently updated seventh edition of Gradshteyn and Ryzhik’s Table of Integrals, Series, and Products and other important reference works. Suggestions from users of the third edition of the Handbook have resulted in the expansion of many sections, and because of the relevance to boundary value problems for the Laplace equation in the plane, a new chapter on conformal mapping, has been added, complete with an atlas of useful mappings.

All disc-based content for this title is now available on the Web.

View full description### Audience

Researchers, students, professionals in applied mathematics, engineering, physics find this reference essential to help them remember all the basic useful formulas and integrals that make life easier.

### Book information

- Published: January 2008
- Imprint: ACADEMIC PRESS
- ISBN: 978-0-12-374288-9

### Reviews

“This book would find a place on the bookshelf of a professional as a nice reference source. The level is appropriate for our physics majors for use as a reference book.” --Professor Bryan H. Suits, Physics Department, Michigan Technological University “...the 4th edition will be more useful for the students, faculty and professionals in mathematics, science and engineering. Jeffrey has written many books and handbooks and has a tremendous reputation as an author...” --Lokenath Debnath, Chair and Professor at University of Texas, Pan American

### Table of Contents

REVISED CONTENTS LIST FOURTH EDITIONQuick Reference List of Frequently Used Data, Useful Identities, Trigonometric Identities, Hyperbolic Identities, Complex Relationships, Derivatives of Elementary functions, Rules of Differentiation and Integration, Standard Integrals, Standard Series, GeometryNumerical, Algebraic, and Analytical Results for Series and Calculus; Functions and Identities; Derivatives of Elementary Functions; Indefinite Integrals of Algebraic Functions ; Indefinite Integrals of Exponential Functions; Indefinite Integrals of Logarithmic Functions; Indefinite Integrals of Hyperbolic Functions; Indefinite Integrals Involving Inverse Hyperbolic Functions; Indefinite Integrals of Trigonometric Functions; Indefinite Integrals of Inverse Trigonometric Functions; (Chapter 11 has been enlarged) The Gamma, Beta,Pi, and Psi Functions and Incomplete Gamma Functions; Elliptic Integrals and Functions; Probability Integrals and the Error Function; Fresnel Integrals, Sine and Cosine Integrals; Definite Integrals; Different Forms of Fourier Series; Bessel Functions(Sections 18.2.8, 18.2.9, 18.4.6 and 18.5.7 ? 18.5.10 are New); Orthogonal Polynomials,(Sections 18.2.8 and 18.2.9 added on Legendre polynomials); Laplace Transformation; Fourier Transform; Numerical Integration; Solutions of Standard Ordinary Differential Equations; Vector Analysis; Systems of Orthogonal Coordinates; Partial Differential Equations and Special Functions; Qualitative Properties of the Heat and Laplace Equations; Solutions of Elliptic, Parabolic, and Hyperbolic Equations; The z-Transform ; Numerical Approximation; (Chapter 30 is a new and fairly large chapter; Conformal Mapping and Boundary Value Problems