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Pringsheim's Theorem

Let C^omega(I) be the set of real analytic functions on I. Then C^omega(I) is a subalgebra of C^infty(I). A necessary and sufficient condition for a function f in C^infty(I) to belong to C^omega(I) is that

|f^((n))(x)|<=k^nn!

for n=0, 1, ... for a suitable constant k.

See also

Analytic Function, Subalgebra

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References

Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 207, 1980.

Referenced on Wolfram|Alpha

Pringsheim's Theorem

Cite this as:

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

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