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I am stuck with the following problem. Every polynomial of degree $d$ can be expressed as $$ p(x) = p_d \binom{x}{d}+ p_{d-1}\binom{x}{d-1} + \cdots + p_0 \binom{x}{0} $$

What is the representation of $$ \binom{x}{i} \binom{x}{j} $$ in such a basis?

I have no idea how to solve this...

  • 1
    The coefficients are the divided differences. See http://en.wikipedia.org/wiki/Newton_polynomial.2012-11-10

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