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Metadata 
bibkey: bender1973limits
authors: Edward A. Bender
year: 1973
title: Central and local limit theorems applied to asymptotic enumeration
doi: 10.1016/0097-3165(73)90038-1
url: https://doi.org/10.1016/0097-3165(73)90038-1
claim: Theorem 2 supplies the real-rooted nonnegative polynomial criterion for central and local normal limits under variance divergence.
strata_touched:
  - D5/S3/Analytic/Probability/UniformCDFConvergence
  - D5/S3/Analytic/Probability/BernoulliTriangularLimits
license: citation-only
triage: anchor

Central and local limit theorems applied to asymptotic enumeration

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DOI: 10.1016/0097-3165(73)90038-1

Source: https://doi.org/10.1016/0097-3165(73)90038-1

Cited result

Zhang and Zhao quote Theorem 2 as their Theorem 4.2, page 9: a real-rooted polynomial sequence with nonnegative coefficients has both normal limit theorems when its variance diverges. The Bernoulli-polynomial result proves the shifted product form of this criterion through characteristic functions and Fourier inversion. The original paper’s full text is not used as an additional proof premise.