عنوان

(Almost) impossible integrals, sums, and series /

3030024628

3030024636

9783030024628

9783030024635

303002461X

9783030024611

(Almost) impossible integrals, sums, and series /

[Book]

Cornel Ioan Vălean.

Cham, Switzerland :

Springer,

[2019]

1 online resource

Problem books in mathematics

Includes bibliographical references and index.

Intro; Foreword; Preface; Contents; 1 Integrals; 1.1 A Powerful Elementary Integral; 1.2 A Pair of Elementary Logarithmic Integrals We Might Find Very Useful for Solving the Problems in the Book; 1.3 Four Logarithmic Integrals Strongly Connected with the League of Harmonic Series; 1.4 Two Very Useful Classical Logarithmic Integrals That May Arise in the Calculation of Some Tough Integrals and Series; 1.5 A Couple of Practical Definite Integrals Expressed in Terms of the Digamma Function; 1.6 A Useful Special Generalized Integral Expressed in Terms of the Polylogarithm Function

1.16 A Double Integral and a Triple Integral, Beautifully Connected with the Advanced Harmonic Series1.17 Let's Take Two Double Logarithmic Integrals with Beautiful Values Expressed in Terms of the Riemann Zeta Function; 1.18 Interesting Integrals Containing the Inverse Tangent Function and the Logarithmic Function; 1.19 Interesting Integrals Involving the Inverse Tangent Function and Dilogarithm Function; 1.20 More Interesting Integrals Involving the Inverse Tangent Function and the Logarithmic Function: The First Part

1.21 More Interesting Integrals Involving the Inverse Tangent Function and the Logarithmic Function: The Second Part1.22 Challenging Integrals Involving arctan(x), log(x), log(1-x), Li2(x), and Li2(x2); 1.23 Two More Special Challenging Integrals Involving arctan(x), log(x), log(1+x), and Li2( -x); 1.24 A Challenging Integral with the Inverse Tangent Function and an Excellent Generalization According to the Even Positive Powers of the Logarithm

1.7 Two Little Tricky Classical Logarithmic Integrals1.8 A Special Trio of Integrals with log2(1-x) and log2(1+x); 1.9 A Darn Integral in Disguise (Possibly Harder Than It Seems to Be?), an Integral with Two Squared Logarithms on the Half of the Unit Interval; 1.10 The Evaluation of a Class of Logarithmic Integrals Using a Slightly Modified Result from Table of Integrals, Series and Products by I.S. Gradshteyn and I.M. Ryzhik Together with a Series Result Elementarily Proved by Guy Bastien

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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.

Springer Nature

com.springer.onix.9783030024628

(Almost) impossible integrals, sums, and series.

9783030024611

Integrals.

Integrals.

MAT034000

PBK

PBK

Vălean, Cornel Ioan

20200823074231.0

pn

[Book]

Y