Müntz's theorem is a generalization of the Weierstrass approximation theorem, which states that any continuous function on a closed
and bounded interval can be uniformly approximated by polynomials
involving constants and any infinite sequence
of powers whose reciprocals
diverge.

In technical language, Müntz's theorem states that the Müntz space
is dense in iff

## See also

Weierstrass Approximation
Theorem
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## References

Borwein, P. and Erdélyi, T. "Müntz's Theorem." §4.2 in *Polynomials
and Polynomial Inequalities.* New York: Springer-Verlag, pp. 171-205,
1995.## Referenced on Wolfram|Alpha

Müntz's Theorem
## Cite this as:

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

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