In Pursuit of Zeta-3 : : The World's Most Mysterious Unsolved Math Problem / / Paul J. Nahin.

• Superior document: Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2021
• VerfasserIn: Nahin, Paul J.,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2021]; ©2021
• Year of Publication: 2021
• Language: English
• Physical Description: 1 online resource (344 p.) :; 23 b/w illus.

An engrossing look at the history and importance of a centuries-old but still unanswered math problemFor centuries, mathematicians the world over have tried, and failed, to solve the zeta-3 problem. Math genius Leonhard Euler attempted it in the 1700s and came up short. The straightforward puzzle asks if there exists a simple symbolic formula for the following: 1+(1/2)^3+(1/3)^3+(1/4)^3+…? But why is this question—the sum of the reciprocals of the positive integers cubed—so important? With his trademark wit and sharp observations, popular math writer Paul Nahin investigates the history and significance of this mathematical conundrum in In Pursuit of Zeta-3.Relying on detailed examples, historical anecdotes, and even occasionally poetry, Nahin sheds light on the richness of the nature of zeta-3. He shows its intimate connections to the Riemann hypothesis, another mathematical mystery that has stumped mathematicians for nearly two centuries. He looks at its links with Euler’s achievements and explores the modern research area of Euler sums, where zeta-3 occurs frequently. An exact solution to the zeta-3 question wouldn’t simply satisfy pure mathematical interest: it would have critical ramifications for applications in physics and engineering, such as quantum electrodynamics. Challenge problems with detailed solutions and MATLAB code are included at the end of each of the book’s sections.Detailing the trials and tribulations of mathematicians who have approached one of the field’s great unsolved riddles, In Pursuit of Zeta-3 will tantalize curious math enthusiasts everywhere.

Table of Contents

Frontmatter -- Contents -- Preface -- CHAPTER 1 Euler’s Problem -- CHAPTER 2 More Wizard Math and the Zeta Function ζ(s) -- CHAPTER 3 Periodic Functions, Fourier Series, and the Zeta Function -- CHAPTER 4 Euler Sums, the Harmonic Series, and the Zeta Function -- Epilogue -- Appendix 1 Solving the Impossible by Changing the Rules -- Appendix 2 Evaluating ʃ0∞ e-t2dt and ʃ∞0e-pt2 -q/t2 -- Appendix 3 Proof That Σ q-1 ∞ Σ∞ n-1 nǂq 1/qn(n-q)Equals Zero -- Appendix 4: Double Integration Reversal Isn’t Always Legal -- Appendix 5 Impossibility Results from Computer Science -- Challenge Problem Solutions -- Acknowledgments -- Index