Application Guide

56 Alphabetical Listing
domain()
Catalog >
Certain functions cannot be used as
arguments for domain(), regardless of
whether they appear explicitly or within
user-defined variables and functions. In the
following example, the expression cannot
be simplified because ∫() is a disallowed
function.
dominantTerm()
Catalog >
dominantTerm(Expr1, Var [, Point]) ⇒
expression
dominantTerm(Expr1, Var [, Point]) |
Var>Point ⇒ expression
dominantTerm(Expr1, Var [, Point]) |
Var<Point ⇒ expression
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 −∞.