 If

where "δ" > 0 is an arbitrary positive constant, then "f"("z") is a lacunary function that cannot be continued outside its circle of convergence.In other words, the sequence {λ"k"} doesn't have to grow as fast as 2"k" for "f"("z") to be a lacunary function – it just has to grow as fast as some geometric progression (1 + δ)"k".A series for which λ"k" grows this quickly is said to contain Hadamard gaps.