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Date: 18-12-2021
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Date: 28-11-2021
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Date: 3-10-2021
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If is a continuous real-valued function on and if any is given, then there exists a polynomial on such that
for all . In words, any continuous function on a closed and bounded interval can be uniformly approximated on that interval by polynomials to any degree of accuracy.
REFERENCES:
Jeffreys, H. and Jeffreys, B. S. "Weierstrass's Theorem on Approximation by Polynomials" and "Extension of Weierstrass's Approximation Theory." §14.08-14.081 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, pp. 446-448, 1988.
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