rsolve should handle hypergeometric inhomogeneous terms

[pedritomelenas]

It seems that so far rsolve can only handle rational inhomogeneous part: rsolve( x(n)-2*x(n-1)-3**n, x(n),[1]) yields

ValueError: Inhomogeneous part should be a rational function of 'n', got '3**n'

It could be nice to have also parts of the form a^nf(n) with a a positive integer and f(n) a polynomial, as in sympy where rsolve( x(n)-2*x(n-1)-3**n, x(n),[1]) ouputs

-2*2**n + 3*3**n

Thank you,
Pedro

[skirpichev]

I think, that's a (trivial) bug. Current implementation should work for hypergeometric terms too.

Also, instead of raising ValueError - there should be (for non-hypergeometric terms) NotImplementedError instead.

[skirpichev]

Issue retitled. Let me know if you think it's not accurate now.

[pedritomelenas]

Better. Thanks

[pedritomelenas]

Thanks, now rsolve(x(n)-2*x(n-1)-3**n,x(n),[1]) works.
However I cannot make it to work for n*3**n: rsolve(x(n)-2*x(n-1)-3**n*n,x(n),[1]) yields an AttributeError.
Thank you,
Pedro

[skirpichev]

hypersimp() call on line 547 fails. If you make simplify(g) - it works:

In [1]: rsolve(f(n)-2*f(n-1)-3**n*n, f(n),[1])
Out[1]: 
   n    n + 1        
7⋅2  + 3     ⋅(n - 2)

However, I think this should be a separate issue.

[skirpichev]

#456