I am trying to perform a 2D discrete convolution of two terms; one a Gaussian and a differentiated Green's function containing Hankel function of first kind and zero order. The convolution is defined as $$p(x,y,t) = f(x,y) * \frac{d}{dt} G(x,y,t)$$ where,

• $f(x,y) = \epsilon e^{ -\alpha (x^2 + y^2) }$
• $\frac{d}{dt}G(x,y,t) = \frac{\omega}{4} \frac{1}{c_0^2 } H_0^{(1)}\left [k\sqrt{x^2+y^2} \right ] e^{-i \omega t}$

The common parameters in these terms are

• $\epsilon=0.5$,
• $\alpha = \frac{log(2)}{2}$
• $\omega = \frac{2\pi}{30}$
• $c = 340.2626486$
• $ k = \omega/c$
• $t = 90$

These terms are from a paper in acoustics. I have tried to perform a discrete convolution but it fails to produced any output except the warning TerminatedEvaluation["RecursionLimit"]. I have attached the workbook which contains the usage of the commandDiscreteConvolve and the convolving variables I have used are $\xi$ and $\eta$.

What would be right way to perform a convolution for these terms? Are there any gotchas which I need to be aware of ?