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can we find a set of Orthogonal Polynomials so in the limit $ n \rightarrow \infty $ satisfty $ \frac{\sin(x)}{x}= \frac{p_{2n}(x)}{p_{2n}(0)} $

the set of orthogonal polynomials satisfy $ \int_{-\infty}^{\infty}dx w(x) P_{n}(x)P_{m}(x)= \delta _{n}^{m} $ and the measure $ w(x) \ge 0 $ and $ w(x)=w(-x) $ is this problem solvable

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Are you sure, that $w(x)$ appears twice under the integral? –  draks ... Apr 18 '12 at 12:36
No it was a mistake :) sorry –  Jose Garcia Apr 18 '12 at 15:05
Maybe something like $p_n ~ 1-x^2/3!+x^4/5!...$. Of course you still have to find a weight $w(x)$. –  Alex R. Apr 18 '12 at 18:33

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