Müntz's Theorem

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 M(Lambda) is dense in C[0,1] iff


See also

Weierstrass Approximation Theorem

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

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Müntz's Theorem

Cite this as:

Weisstein, Eric W. "Müntz's Theorem." From MathWorld--A Wolfram Web Resource.

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