I have a double integral involving a double exponential oscillatory function:
\begin{equation} \int_{-\infty}^{\infty}\int_{-\infty}^{\infty} e^{-iq^3} e^{-q^2}(q+b)\text{sign(q-b)}e^{ib^3} e^{-b^2}dq db \end{equation}
i just used the following code
NIntegrate[$e^{-iq^3}$ $e^{-q^2}$ (q+b) $\text{sign(q-b)}$ $e^{ib^3}$ $e^{-b^2}$,{q,-$\infty$,$\infty$},{b,$-\infty$,$\infty$},Method -> {"DoubleExponentialOscillatory", "SymbolicProcessing" -> 0}]
and it gives the following message
Numerical integration converging too slowly; suspect one of the \
following: singularity, value of the integration is 0, highly \
oscillatory integrand, or WorkingPrecision too small.
I tried using Method -> {"DoubleExponentialOscillatory", "SymbolicProcessing" -> 0} in NIntegrate and it gives the following message
"Method \!\(\"DoubleExponentialOscillatory\"\) works only for \
one-dimensional integrals with infinite ranges. \
\!\(\*ButtonBox[\">>\", Appearance->{Automatic, None}, \
BaseStyle->\"Link\", ButtonData:>\"paclet:ref/NIntegrate\", \
ButtonNote->\"NIntegrate::oscir\"]\)"
How do I use NIntegrate? Thanks in advance