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Narrow-line Seyfert 1 galaxies have been identified by the Fermi Gamma-RaySpace Telescope as a rare class of gamma-ray emitting active galactic nuclei(AGN). The lowest-redshift candidate among them is the source 1H 0323+342. Herewe present quasi-simultaneous Gemini near-infrared and Keck opticalspectroscopy for it, from which we derive a black hole mass based on both thebroad Balmer and Paschen emission lines. We supplement these observations witha NuSTAR X-ray spectrum taken about two years earlier, from which we constrainthe black hole mass based on the short timescale spectral variability. Ourmultiwavelength observations suggest a black hole mass of ~2x10^7 solar masses,which agrees well with previous estimates. We build the spectral energydistribution and show that it is dominated by the thermal and reprocessedemission from the accretion disc rather than the non-thermal jet component. Adetailed spectral fitting with the energy-conserving accretion disc model ofDone et al. constrains the Eddington ratio to L/L_Edd ~ 0.5 for a(non-rotating) Schwarzschild black hole and to L/L_Edd ~ 1 for a Kerr blackhole with dimensionless spin of a*=0.8. Higher spin values and so higherEddington ratios are excluded, since they would strongly overpredict theobserved soft X-ray flux.

On the black hole mass of the gamma-ray emitting narrow-line Seyfert 1 galaxy 1H 0323+342