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 ![C[0,1]](/images/equations/MuentzsTheorem/Inline2.svg)
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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