(Almost) Impossible Integrals, Sums, and Series

  • Cornel Ioan Vălean

Part of the Problem Books in Mathematics book series (PBM)

Table of contents

  1. Front Matter
    Pages i-xxxviii
  2. Cornel Ioan Vălean
    Pages 1-37
  3. Cornel Ioan Vălean
    Pages 39-53
  4. Cornel Ioan Vălean
    Pages 55-277
  5. Cornel Ioan Vălean
    Pages 279-314
  6. Cornel Ioan Vălean
    Pages 315-328
  7. Cornel Ioan Vălean
    Pages 329-536
  8. Back Matter
    Pages 537-539

About this book


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.


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

Authors and affiliations

  • Cornel Ioan Vălean
    • 1
  1. 1.Teremia Mare, Timiş CountyRomania

Bibliographic information

  • DOI
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-02461-1
  • Online ISBN 978-3-030-02462-8
  • Series Print ISSN 0941-3502
  • Series Online ISSN 2197-8506
  • Buy this book on publisher's site