Table of Integrals, Series, and Products

Table of Integrals, Series, and Products
Author: I. S. Gradshteyn
Publisher: Academic Press
Total Pages: 1207
Release: 2014-05-10
Genre: Mathematics
ISBN: 1483265641

Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. This book provides a comprehensive table of integrals. Organized into 17 chapters, this book begins with an overview of elementary functions and discusses the power of binomials, the exponential function, the logarithm, the hyperbolic function, and the inverse trigonometric function. This text then presents some basic results on vector operators and coordinate systems that are likely to be useful during the formulation of many problems. Other chapters consider inequalities that range from basic algebraic and functional inequalities to integral inequalities and fundamental oscillation and comparison theorems for ordinary differential equations. This book discusses as well the important part played by integral transforms. The final chapter deals with Fourier and Laplace transforms that provides so much information about other integrals. This book is a valuable resource for mathematicians, engineers, scientists, and research workers.

Handbook of Special Functions

Handbook of Special Functions
Author: Yury A. Brychkov
Publisher: CRC Press
Total Pages: 702
Release: 2008-05-28
Genre: Mathematics
ISBN: 158488956X

Because of the numerous applications involved in this field, the theory of special functions is under permanent development, especially regarding the requirements for modern computer algebra methods. The Handbook of Special Functions provides in-depth coverage of special functions, which are used to help solve many of the most difficult problems in physics, engineering, and mathematics. The book presents new results along with well-known formulas used in many of the most important mathematical methods in order to solve a wide variety of problems. It also discusses formulas of connection and conversion for elementary and special functions, such as hypergeometric and Meijer G functions.

Special Functions

Special Functions
Author: George E. Andrews
Publisher: Cambridge University Press
Total Pages: 684
Release: 1999
Genre: Mathematics
ISBN: 9780521789882

An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.

(Almost) Impossible Integrals, Sums, and Series

(Almost) Impossible Integrals, Sums, and Series
Author: Cornel Ioan Vălean
Publisher: Springer
Total Pages: 572
Release: 2019-05-10
Genre: Mathematics
ISBN: 3030024628

This book contains a multitude of challenging problems and solutions that are not commonly found in classical textbooks. One goal of the book is to present these fascinating mathematical problems in a new and engaging way and illustrate the connections between integrals, sums, and series, many of which involve zeta functions, harmonic series, polylogarithms, and various other special functions and constants. Throughout the book, the reader will find both classical and new problems, with numerous original problems and solutions coming from the personal research of the author. Where classical problems are concerned, such as those given in Olympiads or proposed by famous mathematicians like Ramanujan, the author has come up with new, surprising or unconventional ways of obtaining the desired results. The book begins with a lively foreword by renowned author Paul Nahin and is accessible to those with a good knowledge of calculus from undergraduate students to researchers, and will appeal to all mathematical puzzlers who love a good integral or series.

Special Functions

Special Functions
Author: Nico M. Temme
Publisher: John Wiley & Sons
Total Pages: 392
Release: 2011-03-01
Genre: Mathematics
ISBN: 1118030818

This book gives an introduction to the classical, well-known special functions which play a role in mathematical physics, especially in boundary value problems. Calculus and complex function theory form the basis of the book and numerous formulas are given. Particular attention is given to asymptomatic and numerical aspects of special functions, with numerous references to recent literature provided.

An Introduction to Special Functions

An Introduction to Special Functions
Author: Carlo Viola
Publisher: Springer
Total Pages: 172
Release: 2016-10-31
Genre: Mathematics
ISBN: 3319413457

The subjects treated in this book have been especially chosen to represent a bridge connecting the content of a first course on the elementary theory of analytic functions with a rigorous treatment of some of the most important special functions: the Euler gamma function, the Gauss hypergeometric function, and the Kummer confluent hypergeometric function. Such special functions are indispensable tools in "higher calculus" and are frequently encountered in almost all branches of pure and applied mathematics. The only knowledge assumed on the part of the reader is an understanding of basic concepts to the level of an elementary course covering the residue theorem, Cauchy's integral formula, the Taylor and Laurent series expansions, poles and essential singularities, branch points, etc. The book addresses the needs of advanced undergraduate and graduate students in mathematics or physics.

Hypersingular Integrals and Their Applications

Hypersingular Integrals and Their Applications
Author: Stefan Samko
Publisher: CRC Press
Total Pages: 382
Release: 2001-10-25
Genre: Mathematics
ISBN: 9780415272681

Hypersingular integrals arise as constructions inverse to potential-type operators and are realized by the methods of regularization and finite differences. This volume develops these approaches in a comprehensive treatment of hypersingular integrals and their applications. The author is a renowned expert on the topic. He explains the basics before building more sophisticated ideas, and his discussions include a description of hypersingular integrals as they relate to functional spaces. Hypersingular Integrals and Their Applications also presents recent results and applications that will prove valuable to graduate students and researchers working in mathematical analysis.

Inside Interesting Integrals

Inside Interesting Integrals
Author: Paul J. Nahin
Publisher: Springer Nature
Total Pages: 542
Release: 2020-06-27
Genre: Science
ISBN: 3030437884

What’s the point of calculating definite integrals since you can’t possibly do them all? What makes doing the specific integrals in this book of value aren’t the specific answers we’ll obtain, but rather the methods we’ll use in obtaining those answers; methods you can use for evaluating the integrals you will encounter in the future. This book, now in its second edition, is written in a light-hearted manner for students who have completed the first year of college or high school AP calculus and have just a bit of exposure to the concept of a differential equation. Every result is fully derived. If you are fascinated by definite integrals, then this is a book for you. New material in the second edition includes 25 new challenge problems and solutions, 25 new worked examples, simplified derivations, and additional historical discussion.

Special Functions of Mathematics for Engineers

Special Functions of Mathematics for Engineers
Author: Larry C. Andrews
Publisher: SPIE Press
Total Pages: 512
Release: 1998
Genre: Mathematics
ISBN: 9780819426161

Modern engineering and physical science applications demand a thorough knowledge of applied mathematics, particularly special functions. These typically arise in applications such as communication systems, electro-optics, nonlinear wave propagation, electromagnetic theory, electric circuit theory, and quantum mechanics. This text systematically introduces special functions and explores their properties and applications in engineering and science.