Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

share|cite|improve this question
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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.