Laplace’s Method, Fourier Analysis, and Random Walks on Z
نویسنده
چکیده
1.1. Stirling’s formula. Laplace’s approach to Stirling’s formula is noteworthy first, because it makes a direct connection with the Gaussian (normal) distribution (whereas in other approaches the Gaussian distribution enters indirectly, or not at all), and second, because it provides a general strategy for the asymptotic approximation of a large class of integrals with a large parameter. Stirling’s formula states that as n→∞,
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