We report an investigation of the extremely metal-poor and C-rich planetary nebula (PN) K648 in the globular cluster M15 using the UV to far-IR data obtained using the Subaru, HST, FUSE, Spitzer, and Herschel. We determined the nebular abundances of ten elements. The enhancement of F ([F/H]=+0.96) is comparable to that of the halo PN BoBn1. The central stellar abundances of seven elements are determined. The stellar C/O ratio is similar to the nebular C/O ratios from recombination line and from collisionally excited line (CEL) within error, and the stellar Ne/O ratio is also close to the nebular CEL Ne/O ratio. We found evidence of carbonaceous dust grains and molecules including Class B 6-9 um and 11.3 um polycyclic aromatic hydrocarbons and the broad 11 um feature. The profiles of these bands are similar to those of the C-rich halo PNe H4-1 and BoBn1. Based on the theoretical model, we determined the physical conditions of the gas and dust and their masses, i.e., 0.048 Msun and 4.95x10^{-7} Msun, respectively. The observed chemical abundances and gas mass are in good agreement with an asymptotic giant branch nucleosynthesis model prediction for stars with an initial 1.25 Msun plus a 2.0x10^{-3} Msun partial mixing zone (PMZ) and stars with an initial mass of 1.5 Msun without a PMZ. The core-mass of the central star is approximately 0.61-0.63 Msun. K648 is therefore likely to have evolved from a progenitor that experienced coalescence or tidal disruption during the early stages of evolution, and became a ~1.25-1.5 Msun blue straggler.
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