divconq - Maple Help

LREtools

 divconq
 find solutions of "divide and conquer" recurrence equations

 Calling Sequence divconq(problem)

Parameters

 problem - problem statement or RESol

Description

 • Solves divide and conquer recurrences, meaning those of the form $Af\left({R}^{n}k\right)+Bf\left({R}^{m}k\right)=0$, where R is either numeric or a name, m and n are integers, and where A and B are independent of k.
 • See the help page for LREtools[REcreate] for the definition of the format of a problem.

Examples

 > $\mathrm{with}\left(\mathrm{LREtools}\right):$
 > $\mathrm{prob}≔\mathrm{REcreate}\left(\left\{y\left(nk\right)=2y\left(k\right)\right\},y\left(k\right),\varnothing \right)$
 ${\mathrm{prob}}{≔}{\mathrm{RESol}}{}\left(\left\{{y}{}\left({n}{}{k}\right){-}{2}{}{y}{}\left({k}\right){=}{0}\right\}{,}\left\{{y}{}\left({k}\right)\right\}{,}{\varnothing }{,}{\mathrm{INFO}}\right)$ (1)
 > $\mathrm{divconq}\left(\mathrm{prob}\right)$
 ${y}{}\left({1}\right){}{{k}}^{\frac{{\mathrm{ln}}{}\left({2}\right)}{{\mathrm{ln}}{}\left({\mathrm{n~}}\right)}}$ (2)
 > $\mathrm{divconq}\left(f\left({r}^{3}k\right)=2f\left({r}^{2}k\right),f\left(k\right),\varnothing \right)$
 ${f}{}\left({1}\right){}{{k}}^{\frac{{\mathrm{ln}}{}\left({2}\right)}{{\mathrm{ln}}{}\left({r}\right)}}$ (3)