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History of asymptotic expansion of Laplace’s method between Laplace and Erdélyi
In 1774 Laplace understood that $I≔∫\textrm{d}x \exp kf(x)$ for $k≫0$ can be estimated if one knows 2-jet of $f$ at its point of maximum (as $I₀ ≔ ∫\textrm{d}x \exp kf₀(x)$ with $f₀$ quadratic with ...
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