MultiSeries

 find the leading term of a generalized series expansion

Parameters

 expr - algebraic expression x - name; the series variable a - algebraic expression; the expansion point

Description

 • The LeadingTerm function computes a function that is equivalent to expr as the variable x tends to its limit point a. If a is not given, it defaults to 0.
 • When the limit of expr is finite and nonzero, LeadingTerm returns this limit.
 • The underlying engine for computing expansions is the MultiSeries[multiseries] function. In particular, the variable x is assumed to tend to its limit point in the manner described in MultiSeries[multiseries].
 • In rare cases, it might be necessary to increase the value of the global variable Order in order to improve the ability of LeadingTerm to solve problems with significant cancellation. This is made explicit by an error message coming from multiseries.
 • It can also happen that the result is wrong because Testzero failed to recognize that the leading coefficient of a multiseries expansion happens to be 0. In those cases, it is necessary to modify this environment variable (see Testzero).
 • The result is in product-of-powers form.

Examples

 > $\mathrm{with}\left(\mathrm{MultiSeries}\right):$
 > $\mathrm{LeadingTerm}\left({x}^{x},x=0\right)$
 ${1}$ (1)
 > $\mathrm{LeadingTerm}\left(\mathrm{sqrt}\left(\mathrm{sin}\left(x\right)\right),x\right)$
 $\sqrt{{x}}$ (2)
 > $\mathrm{LeadingTerm}\left(\frac{\mathrm{\Gamma }\left(x+\mathrm{exp}\left(-x\right)\right)}{\mathrm{\Gamma }\left(x\right)}-1,x=\mathrm{\infty }\right)$
 $\frac{{\mathrm{ln}}{}\left({x}\right)}{{{ⅇ}}^{{x}}}$ (3)