Asymptotics of generalised trinomial coefficients
Stephan Wagner
TL;DR
This paper derives an asymptotic expansion for generalized central trinomial coefficients using singularity analysis, confirming a conjecture by Zhi-Wei Sun.
Contribution
It introduces a method to obtain asymptotic expansions for generalized trinomial coefficients, proving a conjecture through singularity analysis.
Findings
Established an asymptotic expansion for generalized trinomial coefficients.
Confirmed Zhi-Wei Sun's conjecture.
Demonstrated the effectiveness of singularity analysis in combinatorial asymptotics.
Abstract
It is shown how to obtain an asymptotic expansion of the generalised central trinomial coefficient by means of singularity analysis, thus proving a conjecture of Zhi-Wei Sun.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Theories and Applications · Analytic Number Theory Research