A variety of general results concerning possible summability methods are known.

Since then, mathematicians have explored many different summability methods for divergent series.

Silverman-Toeplitz theorem, characterizing matrix summability methods which are regular.

These are called summability methods.

In this case, one may extend the region where equality holds by considering summability methods such as Cesàro summability.

In physics, there are a wide variety of summability methods; these are discussed in greater detail in the article on regularization.

The lack of convergence of the Fourier series has led to the introduction of a variety of summability methods in order to produce convergence.

Banach Space Functionals and Matrix Summability Methods.

The Silverman-Toeplitz theorem characterizes matrix summability methods, which are methods for summing a divergent series by applying an infinite matrix to the vector of coefficients.

Determination of convergence requires the comprehension of pointwise convergence, uniform convergence, absolute convergence, L spaces, summability methods and the Cesàro mean.

In mathematics, the Silverman-Toeplitz theorem, first proved by Otto Toeplitz, is a result in summability theory characterizing matrix summability methods that are regular.

Summability methods include Cesàro summation, (C,k) summation, Abel summation, and Borel summation, in increasing order of generality (and hence applicable to increasingly divergent series).