Application Guide

162 Alphabetical Listing
series()
Catalog >
Point defaults to 0. Point can be ∞ or −∞,
in which cases the expansion is through
degree Order in 1/(Var − Point).
series(...) returns “series(...)” if it is unable
to determine such a representation, such as
for essential singularities such as sin(1/z)
at z=0, e−
1/z
at z=0, or e
z
at z = ∞ or −∞.
If the series or one of its derivatives has a
jump discontinuity at Point, the result is
likely to contain sub-expressions of the
form sign(…) or abs(…) for a real expansion
variable or (-1)
floor(…angle(…)…)
for a complex
expansion variable, which is one ending
with “_”. If you intend to use the series only
for values on one side of Point, then
append the appropriate one of “| Var >
Point”, “| Var < Point”, “| “Var ≥ Point”,
or “Var ≤ Point” to obtain a simpler result.
series() can provide symbolic
approximations to indefinite integrals and
definite integrals for which symbolic
solutions otherwise can't be obtained.
series() distributes over 1st-argument lists
and matrices.
series() is a generalized version of taylor().
As illustrated by the last example to the
right, the display routines downstream of
the result produced by series(...) might
rearrange terms so that the dominant term
is not the leftmost one.
Note: See also dominantTerm(), page 56.
setMode()
Catalog >
setMode(modeNameInteger,
settingInteger) ⇒ integer
setMode(list) ⇒ integer list
Valid only within a function or program.
Display approximate value of π using the
default setting for Display Digits, andthen
display π witha setting of Fix2. Check to see
that the defaultis restored after the
program executes.