sumexpand SciMax Toolbox sumsplitfact

SciMax Toolbox >> summand_to_rec

summand_to_rec

Maxima Function

Calling Sequence

summand_to_rec (summand, k, n)
summand_to_rec(summand,[k,lo,hi],n)

Description

Returns the recurrence sattisfied by the sum

hi
====
\
>     summand
/
====
k = lo

where summand is hypergeometrical in k and n. If lo and hi are omited, they are assumed to be lo = -inf and hi = inf.

To use this function first load the simplify_sum package with load(simplify_sum).

Example:

(%i1) load("simplify_sum")$
(%i2) summand: binom(n,k);
(%o2)                           binomial(n, k)
(%i3) summand_to_rec(summand,k,n);
(%o3)                      2 sm  - sm      = 0
                               n     n + 1
(%i7) summand: binom(n, k)/(k+1);
                                binomial(n, k)
(%o7)                           --------------
                                    k + 1
(%i8) summand_to_rec(summand, [k, 0, n], n);
(%o8)               2 (n + 1) sm  - (n + 2) sm      = - 1
                                n             n + 1
sumexpand SciMax Toolbox sumsplitfact