Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book gives a comprehensive introduction to those parts of the theory of elliptic integrals and elliptic functions which provide illuminating examples in complex analysis, but which are not often covered in regular university courses. These examples form prototypes of major ideas in modern mathematics and were a driving force of the subject in the eighteenth and nineteenth centuries. In addition to giving an account of the main topics of the theory, the book also describes many applications, both in mathematics and in physics. For the reader’s convenience, all necessary preliminaries on basic notions such as Riemann surfaces are explained to a level sufficient to read the book. For each notion a clear motivation is given for its study, answering the question ‘Why do we consider such objects?’, and the theory is developed in a natural way that mirrors its historical development (e.g., ‘If there is such and such an object, then you would surely expect this one’). This feature sets this text apart from other books on the same theme, which are usually presented in a different order. Throughout, the concepts are augmented and clarified by numerous illustrations. Suitable for undergraduate and graduate students of mathematics, the book will also be of interest to researchers who are not familiar with elliptic functions and integrals, as well as math enthusiasts. .

Elliptic functions. --- Elliptic integrals --- Functions, Elliptic --- Integrals, Elliptic --- Transcendental functions --- Functions of complex variables --- Integrals, Hyperelliptic --- Special functions. --- Functions of complex variables. --- Mathematical physics. --- Special Functions. --- Functions of a Complex Variable. --- Mathematical Methods in Physics. --- Special functions --- Mathematical analysis --- Physical mathematics --- Physics --- Mathematics --- Complex variables --- Elliptic functions --- Functions of real variables --- Funcions el·líptiques --- Functions, Special.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book, the much-anticipated sequel to (Almost) Impossible, Integrals, Sums, and Series, presents a whole new collection of challenging problems and solutions that are not commonly found in classical textbooks. As in the author’s previous book, these fascinating mathematical problems are shown in new and engaging ways, 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. Classical problems are shown in a fresh light, with new, surprising or unconventional ways of obtaining the desired results devised by the author. This book is accessible to readers with a good knowledge of calculus, from undergraduate students to researchers. It will appeal to all mathematical puzzlers who love a good integral or series and aren’t afraid of a challenge.

Calculus, Integral --- Series --- Algebra --- Mathematics --- Processes, Infinite --- Sequences (Mathematics) --- Integral calculus --- Differential equations --- Sequences (Mathematics). --- Special functions. --- Number theory. --- Functions of real variables. --- Mathematical physics. --- Engineering mathematics. --- Sequences, Series, Summability. --- Special Functions. --- Number Theory. --- Real Functions. --- Mathematical Methods in Physics. --- Engineering Mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Physical mathematics --- Physics --- Real variables --- Functions of complex variables --- Number study --- Numbers, Theory of --- Special functions --- Mathematical sequences --- Numerical sequences --- Càlcul integral --- Successions (Matemàtica) --- Functions, Special.