TOPICS
Search

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

 f(z)=sum_(j=1)^inftya_jz^(p_j)

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


See also

Regular Point

Explore with Wolfram|Alpha

References

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. https://mathworld.wolfram.com/Ostrowski-HadamardGapTheorem.html

Subject classifications