Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

I'm having difficulty reproducing a stationary phase approximation to an integral.

I have

[tex]\begin{eqnarray}

F_n(y)&=&\int dx x J_0(xy)(e^{ix^{-n}}-1) \\

&\rightarrow_{large y}&\frac{n^{1/(n+1)}y^{-(n+2)/(n+1)}}{\sqrt{n+1}}\exp[-i(n+1)(y/n)^{\frac{n}{n+1}}]

\end{eqnarray}[/tex]

The integral in the first line derives from the radial part of the integral

[tex]F_n(\mathbf{q})=\int d^2b e^{i\mathbf{q}\cdot\mathbf{b}}(e^{i(b_c/b)^n}-1)[/tex]

where [itex]b_c[/itex] is a constant and b is the radial coordinate; I made some headway treating the phase here as a vector equation to get an expression for the stationary modulus b in terms of q but I can't reproduce the second line; I'm not entirely sure how to handle the asymptotic behaviour of the Bessel function (which gives me real sin, cos that don't appear in this expression?) but I may be missing something more fundamental, as this approach doesn't give me the factor (n+1) in the exponential.

Thanks in advance.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Stationary phase approximation

Can you offer guidance or do you also need help?

**Physics Forums | Science Articles, Homework Help, Discussion**