Integrals and Series: Special functions
Author: Anatoliĭ Platonovich Prudnikov
Publisher: CRC Press
Published: 1986
Total Pages: 768
ISBN-13: 9782881240904
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Table of Integrals, Series, and Products
Author: I. S. Gradshteyn
Publisher: Academic Press
Published: 2014-05-10
Total Pages: 1207
ISBN-13: 1483265641
DOWNLOAD EBOOKTable 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 Integrals and Series
Author: Yury A. Brychkov
Publisher: Chapman and Hall/CRC
Published: 2017-10-15
Total Pages: 0
ISBN-13: 9781439828984
DOWNLOAD EBOOKThis handbook presents many known results as well as new classes of integrals, series, power expansions, and productions of elementary and special functions. It shows how modern computer algebra methods are used to solve various problems in science and engineering. The second volume of the set contains formulas devoted to mathematical physics, including the Meijer G-function and properties of hypergeometric functions. Using these tools, readers can evaluate and simplify numerous new integrals and sums.
Handbook of Special Functions
Author: Yury A. Brychkov
Publisher: CRC Press
Published: 2008-05-28
Total Pages: 702
ISBN-13: 158488956X
DOWNLOAD EBOOKBecause 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
Author: George E. Andrews
Publisher: Cambridge University Press
Published: 1999
Total Pages: 684
ISBN-13: 9780521789882
DOWNLOAD EBOOKAn overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.
(Almost) Impossible Integrals, Sums, and Series
Author: Cornel Ioan Vălean
Publisher: Springer
Published: 2019-05-10
Total Pages: 572
ISBN-13: 3030024628
DOWNLOAD EBOOKThis 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.
An Introduction to Special Functions
Author: Carlo Viola
Publisher: Springer
Published: 2016-10-31
Total Pages: 172
ISBN-13: 3319413457
DOWNLOAD EBOOKThe 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.
Special Functions
Author: Nico M. Temme
Publisher: John Wiley & Sons
Published: 2011-03-01
Total Pages: 392
ISBN-13: 1118030818
DOWNLOAD EBOOKThis 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.
The Gamma Function
Author: Emil Artin
Publisher: Courier Dover Publications
Published: 2015-01-28
Total Pages: 52
ISBN-13: 0486803007
DOWNLOAD EBOOKThis brief monograph on the gamma function was designed by the author to fill what he perceived as a gap in the literature of mathematics, which often treated the gamma function in a manner he described as both sketchy and overly complicated. Author Emil Artin, one of the twentieth century's leading mathematicians, wrote in his Preface to this book, "I feel that this monograph will help to show that the gamma function can be thought of as one of the elementary functions, and that all of its basic properties can be established using elementary methods of the calculus." Generations of teachers and students have benefitted from Artin's masterly arguments and precise results. Suitable for advanced undergraduates and graduate students of mathematics, his treatment examines functions, the Euler integrals and the Gauss formula, large values of x and the multiplication formula, the connection with sin x, applications to definite integrals, and other subjects.
Hypersingular Integrals and Their Applications
Author: Stefan Samko
Publisher: CRC Press
Published: 2001-10-25
Total Pages: 382
ISBN-13: 9780415272681
DOWNLOAD EBOOKHypersingular 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.
