The following theorem is suggested by a problem in the theory of probability. 1 Let pu be a sequence of non-negative numbers for which Ylopk-l, and let m= ^fkpk^-. Suppose further that 00 P(x) = p k x k 0 is not a power series in x l for any integer t>l. Then 1-P(x) has no zeros in the circle \ <1, and the series 1
No takes yet. Share an insight, caveat, or question.
Erdös et al. (1949) studied this question.