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.

$\mathrm{series}\left(\sin \left(x\right)\,x\,5\right)$

$x-\frac{1}{6}{x}^3+O\left(x^5\right)$

$\mathrm{type}\left(\,'\mathrm{laurent}'\right)$

$\mathrm{true}$

$\mathrm{series}\left(\frac{1}{\sin \left(x\right)}\,x\,5\right)$

$x^{\mathrm{-1}}+\frac{1}{6}x+O\left(x^3\right)$

$\mathrm{type}\left(\,'\mathrm{laurent}'\right)$

$\mathrm{true}$

$\mathrm{series}\left(\ln \left(x+x^2\right)\,x\,3\right)$

$\ln \left(x\right)+x-\frac{1}{2}{x}^2+O\left(x^3\right)$

$\mathrm{type}\left(\,'\mathrm{laurent}'\right)$

$\mathrm{false}$