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


On 7/28/05 at 2:28 AM, 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)

One way to do this would be to make use of the KroneckerDelta function. For example:

In[11]:=
Sum[Subscript[x, i]*Subscript[x, j]*(1 - KroneckerDelta[i,j]),
      {i, 3}, {j, 3}]
      
Out[11]=
2*Subscript[x, 1]*Subscript[x, 2] + 
2*Subscript[x, 3]*Subscript[x, 2] + 
2*Subscript[x, 1]*Subscript[x, 3]
--
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