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MathGroup Archive 2005

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Re: How to express a Product (special case) in Mathematica?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg59107] Re: [mg59094] How to express a Product (special case) in Mathematica?
  • From: yehuda ben-shimol <bsyehuda at gmail.com>
  • Date: Fri, 29 Jul 2005 00:41:46 -0400 (EDT)
  • References: <200507280628.CAA12454@smc.vnet.net>
  • Reply-to: yehuda ben-shimol <bsyehuda at gmail.com>
  • Sender: owner-wri-mathgroup at wolfram.com

In case of non singular expression that you need to skip, dont skip it
and then divide by this term.
In case it is singular  (as I have seen in the given site) you
generate a list with 1 replacing the skipped expression and then Apply
Times on the list
the following is just a simple (but yet demonstrative enough) for both cases
skipProd1[j_Integer] := Product[f[i], {i, 10}]/f[j](* non singular case *)
skipProd2[j_Integer] := Times @@ Table[If[i == j, 1, f[i]], {i, 10}](*
singular case*)
regards
yehuda

On 7/28/05, vdavidster at gmail.com <vdavidster at gmail.com> wrote:
> If you're familiar with the Lagrange interpolation polynomial, you'll
> know that the coefficient term, phi, is defined as follows:
> 
>             n
> phi_j (t) = TT     (t - t_i)
>             i=0   -----------
>             i!=j  (t_j - t_i)
> 
> Or in LaTeX notation:
> 
> \phi_j(t) = \prod^{n}_{\stackrel{i=0}{i \neq j}} \frac{(t - t_i)}{(t_j
> - t_i)}
> 
> Or in graphical form:
> http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html
> 
> How do I do that in Mathematica?
> How do I specify a product that skips a value in its iterator, i? (i.e.
> i != j)
> 
> Thanks!
> 
> David
> 
>


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