This is documentation for Mathematica 7, which was
based on an earlier version of the Wolfram Language.

# Regularization

 Regularization is an option for Sum and Product that specifies what type of regularization to use.
• 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 regi for the i variable.
The following sum does not converge:
Using Abel regularization will produce a finite value:
In this case the Abel regularized sum does not exist:
However, the stronger Borel regularization produces a finite value:
A regularized value of a divergent product:
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]=
New in 7