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- W2167130441 abstract "Consider the double integral I ( λ α ) = ∫∫ D g ( x , y , α ) e i λ f ( x , y , α ) d x d y , where λ is a large positive variable and α is an auxiliary parameter. We consider the case in which the phase function f(x,y,α) has two simple stationary points (x+(α), y+(α)) and (x–(α), y–(α)) in D, which coalesce at a point (x, y) as α approaches a critical value α. The point (x,y) can either be an interior point of D or a boundary point of D. Asymptotic expansions are derived in both cases, which hold uniformly in a neighbourhood of α. Our derivation is mathematically rigorous." @default.
- W2167130441 created "2016-06-24" @default.
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- W2167130441 date "2000-02-08" @default.
- W2167130441 modified "2023-09-27" @default.
- W2167130441 title "Uniform asymptotic expansions of a double integral: coalescence of two stationary points" @default.
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- W2167130441 doi "https://doi.org/10.1098/rspa.2000.0523" @default.
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