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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: [mg59126] Re: [mg59094] How to express a Product (special case) in Mathematica?
  • From: Pratik Desai <pdesai1 at umbc.edu>
  • Date: Fri, 29 Jul 2005 00:42:21 -0400 (EDT)
  • References: <200507280628.CAA12454@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.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
>
>  
>
Will this work? or for that matter is it correct ? :-)


\!\(dat = {3, 5, 8, 13}\[IndentingNewLine]
  m = Length[dat]\[IndentingNewLine]
  f[x_] =
    Total[\(Table[\[Product]\+\(n = 1\)\%k\((dat[\([k]\)] -
                    x)\)/\(\[Product]\+\(n = 1\)\%k\((dat[\([k]\)] -
                      dat[\([\((k + 1)\)]\)])\)\), {k, 0, m - 1}] //
          Cancel\) // Simplify]\[IndentingNewLine]
  \)

Best regards,


Pratik

PS: You can copy and paste the code in to Mathematica it works fine

-- 
Pratik Desai
Graduate Student
UMBC
Department of Mechanical Engineering
Phone: 410 455 8134



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