tpsform - Maple Help

powseries

 tpsform
 truncated power series form of a formal series

 Calling Sequence tpsform(p, var, order)

Parameters

 p - name of a formal power series var - variable to be used in the truncated series order - (optional) number of terms to which resulting series should be accurate (this defaults to the global variable Order)

Description

 • The function tpsform(p, var, order) creates a truncated power series (a series data structure) in var.  This truncated series is equal to p up to, but not including, the term containing x^order.
 • In some cases tpsform can determine when the series is exact and so it drops the $\mathrm{O}\left({x}^{\mathrm{order}}\right)$ term. Formal power series created using powpoly fall into this category.
 • The command with(powseries,tpsform) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{powseries}\right):$
 > $\mathrm{powcreate}\left(t\left(n\right)=\frac{t\left(n-1\right)}{n},t\left(0\right)=1\right):$
 > $t\left(\mathrm{_k}\right)$
 $\frac{{t}{}\left({\mathrm{_k}}{-}{1}\right)}{{\mathrm{_k}}}$ (1)
 > $\mathrm{tpsform}\left(t,x,6\right)$
 ${1}{+}{x}{+}\frac{{1}}{{2}}{}{{x}}^{{2}}{+}\frac{{1}}{{6}}{}{{x}}^{{3}}{+}\frac{{1}}{{24}}{}{{x}}^{{4}}{+}\frac{{1}}{{120}}{}{{x}}^{{5}}{+}{O}{}\left({{x}}^{{6}}\right)$ (2)