compute the algebraic residue of an expression
residue(f, x=a, n)
arbitrary algebraic expression
algebraic value at which the residue is evaluated
(optional) positive integer
Computes the algebraic residue of the expression f for the variable x around the point a. The residue is defined as the coefficient of 1x−a in the Laurent series expansion of f.
Maple compute the residue by successively performing series expansions at x=a, by default of orders 2,3,6,11,18,27, and then extracts the coefficient of 1x−a. If this is unsuccessful, for example, because f does not have a Laurent expansion, or because order 27 is still too small, the residue command returns unevaluated.
The maximal order of series expansions being tried can be raised by providing a positive integer n as third argument.
In the following example, there is no Laurent expansion.
In the next example, the default order is too small.
The reason is that the series expansion of order 27 does not have enough terms:
Raising the order to 28 helps:
The residue command was updated in Maple 2019.
The n parameter was introduced in Maple 2019.
For more information on Maple 2019 changes, see Updates in Maple 2019.
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