BUILT-IN WOLFRAM LANGUAGE 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 gives .
  • The following setting can be used to specify a regularization procedure for products :
  • "Dirichlet"
  • Regularization->None 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^(th) variable.

ExamplesExamplesopen allclose all

Basic Examples  (3)Basic Examples  (3)

The following sum does not converge:

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Using Abel regularization will produce a finite value:

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

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However, the stronger Borel regularization produces a finite value:

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A regularized value of a divergent product:

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Introduced in 2008
(7.0)