taylor - Maple Help

type/taylor

check for Taylor series

 Calling Sequence type(expr, taylor)

Description

 • The function type/taylor returns true if expr is a series which is a polynomial in the variable in which it was expanded.  An order term may be present.

Examples

 > $\mathrm{series}\left(\mathrm{sin}\left(x\right),x,5\right)$
 ${x}{-}\frac{{1}}{{6}}{}{{x}}^{{3}}{+}{O}{}\left({{x}}^{{5}}\right)$ (1)
 > $\mathrm{type}\left(,'\mathrm{taylor}'\right)$
 ${\mathrm{true}}$ (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)
 > $\mathrm{type}\left(,'\mathrm{taylor}'\right)$
 ${\mathrm{false}}$ (4)
 > $\mathrm{type}\left({x}^{3},'\mathrm{taylor}'\right)$
 ${\mathrm{false}}$ (5)
 > $\mathrm{series}\left(\frac{x}{y},x\right)$
 $\frac{{1}}{{y}}{}{x}$ (6)
 > $\mathrm{type}\left(,'\mathrm{taylor}'\right)$
 ${\mathrm{true}}$ (7)
 > $\mathrm{series}\left(\frac{x}{y},y\right)$
 ${x}{}{{y}}^{{-1}}$ (8)
 > $\mathrm{type}\left(,'\mathrm{taylor}'\right)$
 ${\mathrm{false}}$ (9)