Re: [Maxima-discuss] Fail to understand result of funcsolve

[Michel T. <ta...@lp...>]

As a matter of fact the program bugs because at line 342 one has a 
division by zero due to the fact that product(%a, %l, lo, %n-1) vanishes 
since it is

the product of %l^2/(%l^2+2*l) starting from l=0.  The way to get out of 
this problem is to impose a condition such as f(1)=1, then the product 
starts at

%l=1.  This can be checked by inserting some prints.

solve_rec((n+1)*f[n]-(n-1)*f[n-1]=(n+1)/(n-1),f[n],f(1)=1);

yields after applying factor to the result:

f[n] = ('sum(((%j+1)*(%j+2))/%j,%j,1,n-1)+2)/(n*(n+1))$

Package Zeilberger doesn't seem to allow to compute the sum.

(%i16) GosperSum((%j+1)*(%j+2)/%j,%j,1,n-1);
(%o16)                        NON_GOSPER_SUMMABLE

Le 24/11/2025 à 17:06, Barton Willis via Maxima-discuss a 
écrit :product(%a, %l, lo, %n-1)
> The share package solve_rec is also unable to handle your recursion:

-- 
Michel Talon