5.3. Functional series 5.3.1. Area of convergence of the functional series

Lecture

Row whose members are functions, is called a functional series.

The set of those values of x for which the functional series converges is called the region of convergence of the series.

In the domain of convergence, its sum is a function of x ; therefore, the sum of a functional series is denoted by S ( x ) .

The greatest use in technology are power series and Fourier series.

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5.1.1. Row definition

5.1.2. Amount of row

5.1.3. Necessary sign of convergence of a number series

5.2.2. Sign of dalamber

5.2.3. Cauchy sign

5.2.4. Integral sign of convergence

5.2.5. Signed rows. Sign of Leibniz

5.3.2. Power series

5.3.3. Analytic functions. Taylor and Maclaurin Rows

Examples of solving problems for the section series

5.3. Functional series 5.3.1. Area of ​​convergence of the functional series