The Lagrange Connection

    In numerical analysis, the Lagrange interpolation polynomial is constructed, and it can be shown to be equivalent to the formula in (4), however the hand computations are messy.  If a computer algebra system, such as Mathematica is used, then it is easy to verify that the two forms are equivalent.  First, enter the formula for the Lagrange polynomial

Then enter formula (4)

The above two formulas can be expanded and shown to be equal.

Details

The following Mathematica command will expand  L[x].

If the command   is issued, the result will be identical.  

The following Mathematica command can be used to determine if the two symbolic quantities are equivalent and will return either a Boolean expression of "true" or "false."  Let's see what happens.

(c) John H. Mathews 2004