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BUILT-IN MATHEMATICA SYMBOL
Regularization
Regularization
is an option for Sum and Product that specifies what type of regularization to use.
Details
- 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" 
- 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
variable.
Examplesopen all
Basic Examples (3)
The following sum does not converge:
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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