Ostrowski-Hadamard Gap Theorem

Let 0<p_1<p_2<... be integers and suppose that there exists a lambda>1 such that p_(j+1)/p_j>lambda for j=1, 2, .... Suppose that for some sequence of complex numbers {a_j} the power series


has radius of convergence 1, then no point of partialD is a regular point for f (Krantz 1999, p. 120).

See also

Regular Point

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Krantz, S. G. "The Ostrowski-Hadamard Gap Theorem." §9.2.2 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 119-120, 1999.

Referenced on Wolfram|Alpha

Ostrowski-Hadamard Gap Theorem

Cite this as:

Weisstein, Eric W. "Ostrowski-Hadamard Gap Theorem." From MathWorld--A Wolfram Web Resource.

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