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