On Monday 17 September 2007, you wrote:
> I guess I don't understand your requirement.
When I wrote: "it should be the same expression"
I implicitly meant that I hadn't verified if the expression
given in (%o13) and the one you wanted me to post (%o24)
are the same. I had changed my algorithm producing these expressions.
> What exactly is the
> transformation you are trying to perform? Please give us both the input
> and the output of the transformation.
I was only experimenting with the expressions.
I had no specific transformation in mind.
I thought it would be nice to get the base factorials as you call them below.
I'm still trying to get a nice form, of coefficients
of a non-classical orthogonal polynomial of degree 2, and the expression
I posted is a denominator of a coeffient of that polynomial.
>
> One way to simplify your expression is:
>
> factor(minfactorial(makefact(in)))
>
> which produces the result
>
> a!^2*(b+a+2)^3*(b+a+3)^2*(b+a+4)*(b^3+3*a*b^2+7*b^2+3*a^2*b+18*a*b+20*b+a^3
>+7*a^2+20*a+16)*b!^2*(b+a+1)!^5
>
> ==
>
> (b+a+2)^3*(b+a+3)^2*(b+a+4)
> * a!^2 * b!^2 * (b+a+1)!^5
> *(b^3+3*a*b^2+7*b^2+3*a^2*b+18*a*b+20*b+a^3+7*a^2+20*a+16)
>
> That is, a polynomial times the base factorials, which seems like a nice
> form.
I'll have to simplify the other coefficients first, but I think
this looks really nice. Decreasing powers in the first line.
> From here, it looks like you want to combine terms like
> (b+a+2)*(b+a+1)! => (b+a+2)!, right? The simplest way to do this is
>
> expr: expr*(a+b+4)!/(a+b+4)/(a+b+3)!;
>
> You can write a loop do this systematically, e.g.
>
> substabn(ex):=
> block([newex],
> for i: 1 thru 5 do
> while denom(newex: ex*(a+b+i)!/((a+b+i)*(a+b+i-1)!))=1
> do ex:newex,
> ex)
>
> Applying substabn to the above result, we get
>
>
> a!^2*b!^2*(b+a+1)!^2
> *(b^3+3*a*b^2+7*b^2+3*a^2*b+18*a*b+20*b+a^3+7*a^2+20*a+16)
> *(b+a+2)!*(b+a+3)!*(b+a+4)!
also a nice form.
>
> Is that what you had in mind?
I'll see. For now I'm satisfied.
The background:
e.g the Jacobi polynomials can be generated with a gram-schmidt
orthogonalization process. But somebody someday must have realized
that the 3-term recursion for the Jacobi polynomials can be closed.
And even that this closed form can be derived from a rodriguez formula.
The thing I'm trying to do is to modify the inner product and finding
the closed form, even if there is no rodriguez formula.
>
> -s
Thanks
Andre