engleski

Asymptotic Expansions of Central Binomial Coefficients and Catalan Numbers

We give a systematic view of the asymptotic expansion of two well-known sequences, the central binomial coefficients and the Catalan numbers. The main point is explanation of the nature of the best shift in variable $n$, in order to obtain ``nice'' asymptotic expansions. We also give a complete asymptotic expansion of partial sums of these sequences.

binomial coefficient; Catalan number; asymptotic expanison; gamma function

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