A. D. Polyanin and A. V. Manzhirov, Handbook of Mathematics for Engineers and Scientists, Chapman & Hall/CRC Press, 2006 To book contents

8. Series

• 8.1. Numerical Series and Infinite Products
  • 8.1.1. Convergent Numerical Series and Their Properties. Cauchy's Criterion
  • 8.1.2. Convergence Criteria for Series with Positive (Nonnegative) Terms
  • 8.1.3. Convergence Criteria for Arbitrary Numerical Series. Absolute and Conditional Convergence
  • 8.1.4. Multiplication of Series. Some Inequalities
  • 8.1.5. Summation Methods. Convergence Acceleration
  • 8.1.6. Infinite Products
• 8.2. Functional Series
  • 8.2.1. Pointwise and Uniform Convergence of Functional Series
  • 8.2.2. Basic Criteria of Uniform Convergence. Properties of Uniformly Convergent Series
• 8.3. Power Series
  • 8.3.1. Radius of Convergence of Power Series. Properties of Power Series
  • 8.3.2. Taylor and Maclaurin Power Series
  • 8.3.3. Operations with Power Series. Summation Formulas for Power Series
• 8.4. Fourier Series
  • 8.4.1. Representation of 2π-Periodic Functions by Fourier Series. Main Results
  • 8.4.2. Fourier Expansions of Periodic, Nonperiodic, Odd, and Even Functions
  • 8.4.3. Criteria of Uniform and Mean-Square Convergence of Fourier Series
  • 8.4.4. Summation Formulas for Trigonometric Series
• 8.5. Asymptotic Series
  • 8.5.1. Asymptotic Series of Poincare Type. Formulas for the Coefficients
  • 8.5.2. Operations with Asymptotic Series
• References for Chapter 8

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