SERIES
computes Taylor series, asymptotic development
and limit at finite and infinite points.
It should cover a lot of weird limits, even some that are not handled
by the TI92 (not surprising!) nor by maple (more surprising!) like:
LIMIT
instruction may be used if you need only the limit.
Note that SERIES
handles more limits than LIMIT
, but
is a lot slower for trivial cases. SERIES
can not be used
with non-exact arguments (like 0.1) and should not be used with parameters.
LIMIT
may give strange results with parameters. If you see
a warning message, you will get
a binary integer as answer, this means that SERIES
or LIMIT
was not successful, the binary integer is an error code.
Syntax of SERIES
:
Put on the stack the following arguments in this order
#5d
).
SERIES
, this computes the bidirectional limit at level 3.
At level 2, you get a list of two elements: the series expansion and
the rest order. They are expressed in terms of a small parameter h.
At level 1, h is expressed in terms of the initial variable (hence
calling EXEC
would return the series expansion and the rest in
terms of the initial variable).
EVAL
key) and call the TRUNC
function.
SERIES
will not be successful and returns an error
code. You can look at E for more details about the failure.
DEL
in user mode
or EVAL
.
Examples:
1/x
SERIES
1/x
SERIES
1/x SERIES
x
SERIES
SERIES
x 5
SERIES
x
SERIES
x=0+0
SERIES
The syntax of LIMIT
is similar: put the function and the
'variable=limit_point'
equation on the stack.
Note that you can not force the order
for series expansions and LIMIT
handles only bidirectional
limits (except at infinity). LIMIT
returns only the limit at stack
level 1.
Erable
can handle relatively complex limits, like the example
above (extracted from the Mupad
on-line help):
LIMIT
returns -e2.
In addition Erable
provides the:
TRUNC
instruction which
truncates a series expansion at level 2 with
respect to the rest at level 1.
DIVPC
instruction which make a division in ascending power
up to an integer order. The numerator is at level 3, the denominator
at level 2 and the order at level 1.