In mathematics, the stationary phase approximation is a basic principle of asymptotic analysis, applying to oscillatory integrals
I
(
k
)
=
∫
g
(
x
)
e
i
k
f
(
x
)
d
x
{\displaystyle I(k)=\int g(x)e^{ikf(x)}\,dx}
taken over n-dimensional space ℝn where i is the imaginary unit. Here f and g are real-valued smooth functions. The role of g...
In mathematics, the method of steepest descent or stationary-phase method or saddle-point method is an extension of Laplace's method for approximating an integral, where one deforms a contour integral in the complex plane to pass near a stationary point (saddle point), in roughly the direction of steepest descent or stationary phase. The saddle-point approximation is used with integrals in the complex plane, whereas Laplace’s method is used with real integrals.
The integral to be estimated is often of the form
∫
C
...
