2. A series with the same symbol, and the positive and negative symbols of each item in the series.
3. Generalized harmonic series, that is, P- series, P
4. Sign change series, with emphasis on staggered series.
Leibniz discriminant method is only a special case of Dirichlet discriminant method.
1. For any point a, the function series has a corresponding numerical series, and its convergence and divergence can be judged by the numerical series.
2. If the function series converges or diverges at point A, point A is called the convergence point or divergence point of the function series.
3. The convergence points of the function series are integrated into the convergence domain of the function series. If the convergence domain is an interval, it is called a convergence interval.
4. Uniform convergence
The continuity, differentiability and integrability of function series are studied by the continuity, differentiability and integrability of each term, that is, by studying the whole locally.
5. Uniform Convergence of Function Sequences Cauchy Uniform Convergence Criterion
Function series and function sequence are only different in form, and there is no essential difference.
6. Uniform convergence of function series
Under the condition of uniform convergence, the analytical properties of function series (limit, differentiable and integrable) can be interchanged by infinite sum operation.
1 and the property analysis of power series
2. The conditions and expansions of function expansion into power series.
3. Abel's first theorem: it is pointed out that the convergence point and divergence point of power series cannot be mixed and staggered on the number axis.
4. Convergence radius. The convergence radius of power series is determined by the coefficient of power series.
5. Abel's second theorem: although the power function does not necessarily converge uniformly in the convergence interval, it converges uniformly in any closed interval of the convergence interval, which is called the inner closed uniform convergence property.
6. Properties of power function
1. If a function can be expanded into a power series, what is the relationship between the coefficients of the power series and this function?
2. Under what conditions can a function be expanded into a power series?
3. Binomial expansion formula
4. Application of power series: approximate calculation of number π, approximate calculation of number E, approximate calculation of logarithm and representation of non-elementary functions.
5. Analytic definition of exponential function. Power series is an analytical tool to define exponential function and trigonometric function.
1, orthogonality of trigonometric functions
2. For the interval [-π, π], there are three questions to be confirmed.
2.4, Riemann Lemma
3, piecewise continuous, piecewise smooth