The RESol command calls LREtools[REcreate] to build the RESol data structure.

This data structure represents the solution of a recurrence equation.  It is to rsolve and LREtools as DESol is to dsolve and DEtools.

The parameters of an RESol are a set of normalized equations, a set of function names and a set of initial conditions.

On output, an information table, INFO is added.  The entries in this table are:

Note that the first three items are always present, and the next three are there only if the recurrence is linear.

$\mathrm{RESol}\left(\left\{a\left(n+1\right)-a\left(n\right)=n\right\}\,\left\{a\left(n\right)\right\}\,\varnothing \right)$

$\mathrm{RESol}\left(\left\{a\left(n+1\right)-a\left(n\right)=n\right\}\,\left\{a\left(n\right)\right\}\,\left\{a\left(0\right)=a\left(0\right)\right\}\,\mathrm{INFO}\right)$

$\mathrm{re}≔\mathrm{LREtools}\left[\mathrm{REcreate}\right]\left(a\left(n+2\right)-n^{2}a\left(n+1\right)+\left(n-17\right)a\left(n\right)=\sin \left(n\right)\,a\left(n\right)\,\left\{a\left(0\right)=0\right\}\right)$

$\mathrm{re}≔\mathrm{RESol}\left(\left\{a\left(n+2\right)-n^{2}a\left(n+1\right)+\left(n-17\right)a\left(n\right)=\sin \left(n\right)\right\}\,\left\{a\left(n\right)\right\}\,\left\{a\left(0\right)=0\,a\left(1\right)=a\left(1\right)\right\}\,\mathrm{INFO}\right)$

$\mathrm{print}\left(\mathrm{op}\left(4\,\mathrm{re}\right)\right)$

$table\left(\left[\mathrm{coeffs}=\left[-\sin \left(n\right)\,n-17\,-n^2\,1\right]\,\mathrm{vars}=n\,\mathrm{shifteqn}={{\mathrm{\&Shift}}_n\left(a\right)}^2-n^2{\mathrm{\&Shift}}_n\left(a\right)+n-17\,\mathrm{polycoeffs}=\mathrm{false}\,\mathrm{linear}=\mathrm{true}\,\mathrm{min\_shift}=0\,\mathrm{max\_shift}=2\,\mathrm{order}=2\,\mathrm{nonvars}=\left(\right)\,\mathrm{rhs}=\sin \left(n\right)\,\mathrm{functions}=a\,\mathrm{type}=\mathrm{constcoeffs}\right]\right)$

$\mathrm{re2}≔\mathrm{LREtools}\left[\mathrm{REcreate}\right]\left({a\left(n+2\right)}^2-a\left(n\right)=0\,a\left(n\right)\,\varnothing \right)$

$\mathrm{re2}≔\mathrm{RESol}\left(\left\{{a\left(n+2\right)}^2-a\left(n\right)=0\right\}\,\left\{a\left(n\right)\right\}\,\varnothing \,\mathrm{INFO}\right)$

$\mathrm{print}\left(\mathrm{op}\left(4\,\mathrm{re2}\right)\right)$

$table\left(\left[\mathrm{vars}=n\,\mathrm{linear}=\mathrm{false}\,\mathrm{min\_shift}=0\,\mathrm{max\_shift}=2\,\mathrm{order}=2\,\mathrm{nonvars}=\left(\right)\,\mathrm{functions}=a\right]\right)$