Sorry Richard for not answering your suggestions,
Some minutes ago I realized that your e-mails were
put in a spam folder by my mail account provider.
I'm a step further, see below.
On Monday 17 September 2007, andre maute wrote:
> 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
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