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    Stirling asymptotics of $\binom{2N}{N}$ and $\log\binom{N}{m}$

    P-TRIV-CA30

    Area
    Complex Analysis
    Status
    draft
    Contents

    Using Stirling’s approximation, find the leading behavior of:

    1. \(\binom { 2 N } { N }\) for large N.

    2. \(S = \log Z ( N , m )\) with \(\begin{array} { r } { Z = \frac { N ! } { ( N - m ) ! m ! } } \end{array}\) for large N.

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