A function, continuous in a finite closed interval, can be approximated with a preassigned accuracy by polynomials. A function of a real variable which is continuous and has period can be approximated by trigonometric polynomials.

# Weierstrass's Polynomial Theorem

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## References

Szegö, G.*Orthogonal Polynomials, 4th ed.*Providence, RI: Amer. Math. Soc., p. 5, 1975.

## Referenced on Wolfram|Alpha

Weierstrass's Polynomial Theorem## Cite this as:

Weisstein, Eric W. "Weierstrass's Polynomial Theorem." From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/WeierstrasssPolynomialTheorem.html