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Regularization

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

The following settings can be used to specify regularization procedures for sums of the form :

The following setting can be used to specify a regularization procedure for products :

"Dirichlet"

For multiple sums and products, the same regularization is by default used for each 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]=