Aims: We describe our newly developed approach to detailed abundance analysis from integrated-light high-dispersion spectra of star clusters. As a pilot project, we measure abundances of several elements for three globular clusters (GCs) in the Fornax dSph, using VLT/UVES spectra. Methods: We divide the cluster colour-magnitude diagrams into about 100 bins and compute synthetic spectra for each bin. The individual model spectra are co-added and the abundances are iteratively adjusted until the best match to the observed spectra is achieved. Results: We find [Fe/H] = -2.3, -1.4 and -2.1 for Fornax 3, 4 and 5, with +/-0.1 dex uncertainties. Fornax 3 and 5 are thus similar in metallicity to the most metal-poor Milky Way GCs and fall near the extreme metal-poor end of the field star metallicity distribution in Fornax. The [alpha/Fe] ratios, as traced by Ca and Ti, are enhanced with respect to the Solar composition at the level of about +0.25 dex for Fornax 3 and 5, and possibly slightly less (about +0.12 dex) for Fornax 4. For all three clusters the [Mg/Fe] ratio is significantly less elevated than [Ca/Fe] and [Ti/Fe], possibly an effect of the abundance anomalies that are well-known in Galactic GCs. We thus confirm that Mg may be a poor proxy for the overall alpha-element abundances for GCs. The abundance patterns of heavy elements (Y, Ba and Eu) indicate a dominant contribution to nucleosynthesis from the r-process in all three clusters, with a mean [Ba/Eu]=-0.7, suggesting rapid formation of the GCs. Conclusions: Combining our results with literature data for Fornax 1 and 2, four of the five Fornax GCs fall in the range -2.5<[Fe/H]<-2, while Fornax 4 is substantially more metal-rich than the others. The indications that abundance anomalies are detectable in integrated light are encouraging, particularly for the prospects of detecting such anomalies in young, massive star clusters.
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