Excursions in classical analysis [electronic resource] : pathways to advanced problem solving and undergraduate research / Hongwei Chen.

By: Contributor(s): Material type: TextTextSeries: Classroom resource materials (Unnumbered)Publication details: Washington, D.C. : Mathematical Association of America, c2010.Description: xiii, 301 p. : illSubject(s): Genre/Form: LOC classification:
  • QA301 .C436 2010eb
Online resources:
Contents:
Two classical inequalities -- A new approach for proving inequalities -- Means generated by an integral -- The L'Hôpital monotone rule -- Trigonometric identities via complex numbers -- Special numbers -- On a sum of cosecants -- The gamma products in simple closed forms -- On the telescoping sums -- Summation of subseries in closed form -- Generating functions for powers of Fibonacci numbers -- Identities for the Fibonacci powers -- Bernoulli numbers via determinants -- On some finite trigonometric power sums -- Power series of (arcsin x)² -- Six ways to sum [zeta] 2 -- Evaluations of some variant Euler sums -- Interesting series involving binomial coefficients -- Parametric differentiation and integration -- Four ways to evaluate the Poisson integral -- Some irresistible integrals.
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Includes bibliographical references and index.

Two classical inequalities -- A new approach for proving inequalities -- Means generated by an integral -- The L'Hôpital monotone rule -- Trigonometric identities via complex numbers -- Special numbers -- On a sum of cosecants -- The gamma products in simple closed forms -- On the telescoping sums -- Summation of subseries in closed form -- Generating functions for powers of Fibonacci numbers -- Identities for the Fibonacci powers -- Bernoulli numbers via determinants -- On some finite trigonometric power sums -- Power series of (arcsin x)² -- Six ways to sum [zeta] 2 -- Evaluations of some variant Euler sums -- Interesting series involving binomial coefficients -- Parametric differentiation and integration -- Four ways to evaluate the Poisson integral -- Some irresistible integrals.

Electronic reproduction. Palo Alto, Calif. : ebrary, 2013. Available via World Wide Web. Access may be limited to ebrary affiliated libraries.

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