I was having a look at the DLMF chapter on integrals with coalescing saddles, and there are a few things that I’d like to try out with the functions it describes, including e.g. the Pearcey integral, $ $ \Psi_{2}\left(\mathbf{x}\right)=P(x_{2},x_{1})=\int_{-\infty}^{\infty} \exp\left(\mathrm{i}(t^{4}+x_{2}t^{2}+x_{1}t)\right)\mathrm{d}t, $ $ or the elliptic and hyperbolic umbilic catastrophe integrals, $ $ \Psi^{(\mathrm{E})}\left(x,y,z\right)=\int_{-\infty}^{\infty}\int_{-\infty}^{\infty} \exp\left(i\left(s^3-3⁢s⁢t^2+z⁢(s^2+t^2)+y⁢t+x⁢s \right)\right)\mathrm{d}s\,\mathrm{d}t $ $ and $ $ \Psi^{(\mathrm{H})}\left(x,y,z\right)=\int_{-\infty}^{\infty}\int_{-\infty}^{\infty} \exp\left(i\left(s^3+t^3+zst+yt+xs,\right)% \right)\mathrm{d}s\,\mathrm{d}t, $ $ and I was wondering whether they are implemented in the core Wolfram language and in Mathematica (which doesn’t appear to be the case) or in reasonably standard packages. What good resources are available for accessing these functions in Mathematica?