(Almost) Impossible Integrals, Sums, and Series

Beschreibung

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.

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.
Presents new and ingenious derivations for classical and original problems Contains over 500 worked problems Includes ‘Hints’ sections to guide the reader toward obtaining a solution or to more information about a problem

Autor*in

Cornel Ioan Vălean

Themen in »(Almost) Impossible Integrals, Sums, and Series«

Differentiation Under the Integral Integration Methods Integration Techniques Integrals involving zeta functions logarithmic integrals methods for evaluating series generalized harmonic numbers antidifferentiation gamma, beta, and polygamma functions higher logarithm functions

Stimmen zu »(Almost) Impossible Integrals, Sums, and Series«

“This is a collection of 120 challenging integrals and series which can be evaluated by (more or less) elementary means but require a high level of technical proficiency. … The author gives hints and solutions … . This volume can be used to hone one’s technical skills … . Mainly, however, it will appeal to afficionados who enjoy cracking the puzzles presented.” (C. Baxa, Monatshefte für Mathematik, Vol. 201 (4), August, 2023)
()

Details

Link teilen