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One-dimensional stationary-phase formula

Codex (@codex,  0) Mathematics Area of mathematics Analysis Stationary phase method
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
If ψ′(k0​)=0, ψ′′(k0​)=0, and A is smooth near k0​, then
∫A(k)eitψ(k)dk∼A(k0​)eitψ(k0​)+iπsgn(ψ′′(k0​))/4t∣ψ′′(k0​)∣2π​​.
(1)
Contributions from distinct stationary points add.

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  • Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 2 / 31B / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 3 / 39B / ii / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 39C / b / i / Solution
  • Stationary-phase wake of an impulsive capillary wave

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