We study integral representations of the Gevrey series solutions of irregular hypergeometric systems. In this paper we consider the case of the systems associated with a one row matrix, for which the integration domains are one dimensional. We prove
that any Gevrey series solution along the singular support of the system is the asymptotic expansion of a holomorphic solution given by a carefully chosen integral representation.
The first map of interstellar acetylene (C2H2) has been obtained with the infrared spectrograph onboard the Spitzer Space Telescope. A spectral line map of the $ u_5$ vibration-rotation band at 13.7 microns carried out toward the star-forming region
Cepheus A East, shows that the C2H2 emission peaks in a few localized clumps where gas-phase CO2 emission was previously detected with Spitzer. The distribution of excitation temperatures derived from fits to the C2H2 line profiles ranges from 50 to 200 K, a range consistent with that derived for gaseous CO2 suggesting that both molecules probe the same warm gas component. The C2H2 molecules are excited via radiative pumping by 13.7 microns continuum photons emanating from the HW2 protostellar region. We derive column densities ranging from a few x 10^13 to ~ 7 x 10^14 cm^-2, corresponding to C2H2 abundances of 1 x 10^-9 to 4 x 10^-8 with respect to H2. The spatial distribution of the C2H2 emission along with a roughly constant N(C2H2)/N(CO2) strongly suggest an association with shock activity, most likely the result of the sputtering of acetylene in icy grain mantles.
