Texas Instruments TI-Nspire CAS, Reference Manual, Page: 59 / 276

dominantTerm()
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Returns the dominant term of a power
series representation of
Expr1 expanded
about Point . The dominant term is the one
whose magnitude grows most rapidly near
Var = Point . The resulting power of ( Var −
Point ) can have a negative and/or
fractional exponent. The coefficient of this
power can include logarithms of (
Var −
Point ) and other functions of Var that are
dominated by all powers of ( Var − Point )
having the same exponent sign.
Point defaults to 0. Point can be ∞ or −∞ ,
in which cases the dominant term will be
the term having the largest exponent of
Var
rather than the smallest exponent of
Var .
dominantTerm(…) returns “ dominantTerm
(…)
” 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 dominant
term only for values on one side of
Point
,
then append to
dominantTerm(
...
)
the
appropriate one of “| Var > Point ”, “| Var
<
Point
”, “| “
Var ≥ Point
”, or “
Var ≤
Point ” to obtain a simpler result.
dominantTerm() distributes over 1st-
argument lists and matrices.
dominantTerm()
is useful when you want to
know the simplest possible expression that
is asymptotic to another expression as
Var → Point . dominantTerm() is also useful
when it isn’t obvious what the degree of
the first non-zero term of a series will be,
and you don’t want to iteratively guess
either interactively or by a program loop.
Alphabetical Listing 59