find the leading term of a series expansion

Parameters

 expr - expression eqn - equation (such as $x=a$) or name (such as x) n - (optional) non-negative integer

Description

 • The series function computes a truncated series expansion of expr, with respect to the variable x, about the point a, up to order n.
 • If the third argument n is present then it specifies the truncation order'' of the series. If n is not present, the truncation order'' is determined by the global variable Order. The user may assign any non-negative integer to Order.  The default value of Order is 6.
 • If the first argument to series consists of a function call to leadterm, then only the first (the lowest degree) term of the series of expr is computed.
 • When series is invoked with leadterm, it is still subject to the constraint of the global variable Order; the series will only be computed up to degree Order. Thus, if series/leadterm is called on an expression whose leading term is of higher degree than Order, an error results. However, Order may be set arbitrarily high when using the leadterm option, without wasted computation, since only the first term is actually computed.

Examples

 > $\mathrm{int}\left(\mathrm{exp}\left({x}^{3}\right),x\right)$
 ${-}\frac{{\left({-1}\right)}^{{2}}{{3}}}{}\left(\frac{{2}{}{x}{}{\left({-1}\right)}^{{1}}{{3}}}{}{\mathrm{\pi }}{}\sqrt{{3}}}{{3}{}{\mathrm{\Gamma }}{}\left(\frac{{2}}{{3}}\right){}{\left({-}{{x}}^{{3}}\right)}^{{1}}{{3}}}}{-}\frac{{x}{}{\left({-1}\right)}^{{1}}{{3}}}{}{\mathrm{\Gamma }}{}\left(\frac{{1}}{{3}}{,}{-}{{x}}^{{3}}\right)}{{\left({-}{{x}}^{{3}}\right)}^{{1}}{{3}}}}\right)}{{3}}$ (1)
 > $\mathrm{series}\left('\mathrm{leadterm}'\left(\right),x=0\right)$
 ${x}$ (2)
 > $\mathrm{series}\left('\mathrm{leadterm}'\left({x}^{x}\right),x=0,3\right)$
 ${1}$ (3)
 > $\mathrm{sqrt}\left(\mathrm{sin}\left(x\right)\right)$
 $\sqrt{{\mathrm{sin}}{}\left({x}\right)}$ (4)
 > $\mathrm{series}\left('\mathrm{leadterm}'\left(\right),x=0,4\right)$
 $\sqrt{{x}}$ (5)