Elegant Techniques for Zeta and Harmonic Series: A new accessible approach to the Basel problem, Euler sums, and Plouffe identities

Rediscover Zeta and Harmonic Series Through a Bold New Algebraic PerspectiveThe Basel Problem was famously solved by Euler, who unveiled the beauty of even zeta values and odd beta values. Since then, the landscape of infinite series has expanded through the work of many great mathematicians like Dirichlet, Ramanujan, or Zagier, among many others-often requiring advanced and heavy machinery.What if there was a simpler way?This book introduces a compelling alternative technique that naturally unifies these famous results. By focusing on the algebraic interrelations between quantities, this method sheds new light on the links between particular integer zeta values, Euler sums, and Plouffe identities.The best part? You'll find yourself absorbed while exploring the different paths each chapter opens.Whether you are a student or a seasoned researcher, this book provides a fresh toolkit for evaluating series and leaves you with open questions ready to be taken to the next frontier of mathematical discovery.