Generalized series expansions
This functionality does not run in MATLAB.
Series::gseries(f
,x
, <order
>, <Left  Right
>) Series::gseries(f
,x = a
, <order
>, <Left  Right
>)
Series::gseries
is the domain of series expansions
generalizing Taylor, Laurent and Puiseux expansions.
The call Series::gseries(f, x)
computes a
series expansion at the right hand side of x =
0.
The system functions series
and asympt
are the main
application of this domain. The latter function only returns elements
of this domain, whereas series
can return an element
of Series::gseries
in cases, where a Puiseux series
expansion does not exist.
There may be no need to explicitly create elements of this domain, but to work with the results of the mentioned system functions.
See the help page of the system function asympt
for a detailed description of
the parameters and examples for working with elements of the domain Series::gseries
.
Note:
Note that elements of 
The function is sensitive to the global variable ORDER
,
which determines the default number of terms of the expansion.

An arithmetical expression 

The series variable: an identifier 

The expansion point: an arithmetical expression or ± 

The truncation order: a nonnegative integer 

Compute a series expansion that is valid for real x smaller than a. 

Compute a series expansion that is valid for real x larger than a (the default case). 
Object of domain type Series::gseries
, or
the value FAIL
.
Calling an element of Series::gseries
as
a function yields the object itself, regardless of the arguments.
The arguments are not evaluated.
Series::gseries
implements standard arithmetic
of generalized series expansions. Use the ordinary arithmetical operators +
, 
, *
, /
,
and ^
.
The system functions coeff
, lcoeff
, nthcoeff
, lterm
, nthterm
, lmonomial
, nthmonomial
, and ldegree
work on generalized
series expansions. See the corresponding help pages of these functions
for calling parameters. See the description of these methods below
for further details.
The method "indet"
returns the series variable
of the series expansion, i.e., if s
is an object
of the domain Series::gseries
, then s::dom::indet(s)
returns
the series variable.
The method "point"
returns the expansion
point of the series.
Use the function expr
to
convert a generalized series expansion into an arithmetical expression
(as an element of a kernel domain).
A series of the domain type Series::gseries
consists
of four operands:
A list of pairs [c_{i}, f_{i}].
Each pair represents a monomialc_{i} f_{i} of
the series expansion, where the c_{i} are
the coefficients and f_{i} the terms of s
.
The coefficients do not contain the series variable.
This list can be empty, if the order of the expansion is zero.
An arithmetical expression g
representing
the error term of the form O(g).
It may be the integer 0, in which case the expansion is exact.
The series variable x
.
The expansion point a
.