reduce_consts SciMax Toolbox refcheck

SciMax Toolbox >> reduce_order

reduce_order

Maxima Function

Calling Sequence

reduce_order (rec, sol, var)

Description

Reduces the order of linear recurrence rec when a particular solution sol is known. The reduced reccurence can be used to get other solutions.

Example:

(%i3) rec: x[n+2] = x[n+1] + x[n]/n;
                                      x
                                       n
(%o3)               x      = x      + --
                     n + 2    n + 1   n
(%i4) solve_rec(rec, x[n]);
WARNING: found some hypergeometrical solutions!
(%o4)                    x  = %k  n
                          n     1
(%i5) reduce_order(rec, n, x[n]);
(%t5)                    x  = n %z
                          n       n
                           n - 1
                           ====
                           \
(%t6)                %z  =  >     %u
                       n   /        %j
                           ====
                           %j = 0
(%o6)             (- n - 2) %u     - %u
                              n + 1     n
(%i6) solve_rec((n+2)*%u[n+1] + %u[n], %u[n]);
                                     n
                            %k  (- 1)
                              1
(%o6)                 %u  = ----------
                        n    (n + 1)!
So the general solution is
             n - 1
             ====        n
             \      (- 1)
       %k  n  >    -------- + %k  n
         2   /     (n + 1)!     1
             ====
             n = 0
reduce_consts SciMax Toolbox refcheck