An Introduction to Infinite Products

This text provides a detailed presentation of the main results for infinite products, as well as several applications. The target readership is a student familiar with the basics of real analysis of a single variable and a first course in complex analysis up to and including the calculus of residues. The book provides a detailed treatment of the main theoretical results and applications with a goal of providing the reader with a short introduction and motivation for present and future study. While the coverage does not include an exhaustive compilation of results, the reader will be armed with an understanding of infinite products within the course of more advanced studies, and, inspired by the sheer beauty of the mathematics. The book will serve as a reference for students of mathematics, physics and engineering, at the level of senior undergraduate or beginning graduate level, who want to know more about infinite products. It will also be of interest to instructors who teach courses that involve infinite products as well as mathematicians who wish to dive deeper into the subject. One could certainly design a special-topics class based on this book for undergraduates. The exercises give the reader a good opportunity to test their understanding of each section.

Exercises give readers ample opportunity to test their understanding of the material in each section Provides a comprehensive treatment and a solid reference on infinite products, sequences, and series Introduces the necessary concepts and appropriate background

Auteur

Charles Little and Teo L. Kee are Emeritus professors of Mathematics at Massey University in New Zealand. Bruce van Brunt is professor and head of the Mathematics at Massey University in New Zealand.

Résumé
"This is an excellent textbook ... . It must be very satisfactory for students to learn the subject from such a nicely written book." (Marcel G. de Bruin, zbMATH 1491.40001, 2022)

Contenu
Preface.- 1. Introduction.- 2. Infinite Products.- 3. The Gamma Function.- 4. Prime Numbers, Partitions and Products.- 5. Epilogue.- 6. Tables of Products.- References.