laurent - Maple Help

type/laurent

check for Laurent series

 Calling Sequence type(expr, laurent)

Parameters

 expr - expression

Description

 • The call type(expr, laurent) returns true if expr is of type series and only contains power terms of the variable in which it was expanded.
 • In mathematical terminology it returns true if expr is a Laurent series with finite principal part, since type series in Maple represents series with only a finite number of negative powers and with an order-term representing the truncation of a potentially infinite number of positive power terms.

Examples

 > $\mathrm{series}\left(\mathrm{sin}\left(x\right),x,5\right)$
 ${x}{-}\frac{{1}}{{6}}{}{{x}}^{{3}}{+}{O}{}\left({{x}}^{{5}}\right)$ (1)
 > $\mathrm{type}\left(,'\mathrm{laurent}'\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{series}\left(\frac{1}{\mathrm{sin}\left(x\right)},x,5\right)$
 ${{x}}^{{-1}}{+}\frac{{1}}{{6}}{}{x}{+}{O}{}\left({{x}}^{{3}}\right)$ (3)
 > $\mathrm{type}\left(,'\mathrm{laurent}'\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{series}\left(\mathrm{ln}\left(x+{x}^{2}\right),x,3\right)$
 ${\mathrm{ln}}{}\left({x}\right){+}{x}{-}\frac{{1}}{{2}}{}{{x}}^{{2}}{+}{O}{}\left({{x}}^{{3}}\right)$ (5)
 > $\mathrm{type}\left(,'\mathrm{laurent}'\right)$
 ${\mathrm{false}}$ (6)