BUILT-IN MATHEMATICA SYMBOL

# Regularization

Regularization
is an option for Sum and Product that specifies what type of regularization to use.

## DetailsDetails

• Regularization affects only results for divergent sums and products.
• The following settings can be used to specify regularization procedures for sums of the form :
•  "Abel" "Borel" "Cesaro" "Dirichlet"
• For alternating sums , the setting "Euler" gives .
• The following setting can be used to specify a regularization procedure for products :
•  "Dirichlet"
• specifies that no regularization should be used.
• For multiple sums and products, the same regularization is by default used for each variable.
• Regularization->{reg1, reg2, ...} specifies regularization for the i variable.

## ExamplesExamplesopen allclose all

### Basic Examples (3)Basic Examples (3)

The following sum does not converge:

 Out[1]=

Using Abel regularization will produce a finite value:

 Out[2]=

In this case the Abel-regularized sum does not exist:

 Out[1]=

However, the stronger Borel regularization produces a finite value:

 Out[2]=

A regularized value of a divergent product:

 Out[1]=