Excursions in Classical Analysis : Pathways to Advanced Problem Solving.

cover -- copyright page -- title page -- Contents -- Preface -- Two Classical Inequalities -- AM-GM Inequality -- Cauchy-Schwarz Inequality -- Exercises -- References -- A New Approach for Proving Inequalities -- Exercises -- References -- Means Generated by an Integral -- Exercises -- References -- The L'Hôpital Monotone Rule -- Exercises -- References -- Trigonometric Identities via Complex Numbers -- A Primer of complex numbers -- Finite Product Identities -- Finite Summation Identities -- Euler's Infinite Product -- Sums of inverse tangents -- Two Applications -- Exercises -- References -- Special Numbers -- Generating Functions -- Fibonacci Numbers -- Harmonic numbers -- Bernoulli Numbers -- Exercises -- References -- On a Sum of Cosecants -- A well-known sum and its generalization -- Rough estimates -- Tying up the loose bounds -- Final Remarks -- Exercises -- References -- The Gamma Products in Simple Closed Forms -- Exercises -- References -- On the Telescoping Sums -- The sum of products of arithmetic sequences -- The sum of products of reciprocals of arithmetic sequences -- Trigonometric sums -- Some more telescoping sums -- Exercises -- References -- Summation of Subseries in Closed Form -- Exercises -- References -- Generating Functions for Powers of Fibonacci Numbers -- Exercises -- References -- Identities for the Fibonacci Powers -- Exercises -- References -- Bernoulli Numbers via Determinants -- Exercises -- References -- On Some Finite Trigonometric Power Sums -- Sums involving sec^{2p}(k pi /n) -- Sums involving csc^{2p} (k pi/n) -- Sums involving tan^{2p} (k pi/n) -- Sums involving cot^{2p} (k pi/n) -- Exercises -- References -- Power Series of (arcsin x)^2 -- First Proof of the Series (15.1) -- Second Proof of the Series (15.1) -- Exercises -- References -- Six Ways to Sum zeta(2) -- Euler's Proof -- Proof by Double Integrals.

Proof by Trigonometric Identities -- Proof by Power Series -- Proof by Fourier Series -- Proof by Complex Variables -- Exercises -- References -- Evaluations of Some Variant Euler Sums -- Exercises -- References -- Interesting Series Involving Binomial Coefficients -- An integral representation and its applications -- Some Extensions -- Searching for new formulas for -- Exercises -- References -- Parametric Differentiation and Integration -- Example 1 -- Example 2 -- Example 3 -- Example 4 -- Example 5 -- Example 6 -- Example 7 -- Example 8 -- Example 9 -- Example 10 -- Exercises -- References -- Four Ways to Evaluate the Poisson Integral -- Using Riemann Sums -- Using A Functional Equation -- Using Parametric Differentiation -- Using Infinite Series -- Exercises -- References -- Some Irresistible Integrals -- Monthly Problem 10611 -- Monthly Problem 11206 -- Monthly Problem 11275 -- Monthly Problem 11277 -- Monthly Problem 11322 -- Monthly Problem 11329 -- Monthly Problem 11331 -- Monthly Problem 11418 -- Exercises -- References -- Solutions to Selected Problems -- Chapter 1 -- Chapter 2 -- Chapter 3 -- Chapter 4 -- Chapter 5 -- Chapter 6 -- Chapter 7 -- Chapter 8 -- Chapter 9 -- Chapter 10 -- Chapter 11 -- Chapter 12 -- Chapter 13 -- Chapter 14 -- Chapter 15 -- Chapter 16 -- Chapter 17 -- Chapter 18 -- Chapter 19 -- Chapter 20 -- Chapter 21 -- Index -- About the Author.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.