  We validate the discovery of a 2 Earth radii sub-Neptune-size planet around
the nearby high proper motion M2.5-dwarf G 9-40 (EPIC 212048748), using
high-precision near-infrared (NIR) radial velocity (RV) observations with the
Habitable-zone Planet Finder (HPF), precision diffuser-assisted ground-based
photometry with a custom narrow-band photometric filter, and adaptive optics
imaging. At a distance of $d=27.9\mathrm{pc}$, G 9-40b is the second closest
transiting planet discovered by K2 to date. The planet's large transit depth
($\sim$3500ppm), combined with the proximity and brightness of the host star at
NIR wavelengths (J=10, K=9.2) makes G 9-40b one of the most favorable
sub-Neptune-sized planet orbiting an M-dwarf for transmission spectroscopy with
JWST, ARIEL, and the upcoming Extremely Large Telescopes. The star is
relatively inactive with a rotation period of $\sim$29 days determined from the
K2 photometry. To estimate spectroscopic stellar parameters, we describe our
implementation of an empirical spectral matching algorithm using the
high-resolution NIR HPF spectra. Using this algorithm, we obtain an effective
temperature of $T_{\mathrm{eff}}=3404\pm73$K, and metallicity of
$\mathrm{[Fe/H]}=-0.08\pm0.13$. Our RVs, when coupled with the orbital
parameters derived from the transit photometry, exclude planet masses above
$11.7 M_\oplus$ with 99.7% confidence assuming a circular orbit. From its
radius, we predict a mass of $M=5.0^{+3.8}_{-1.9} M_\oplus$ and an RV
semi-amplitude of $K=4.1^{+3.1}_{-1.6}\mathrm{m\:s^{-1}}$, making its mass
measurable with current RV facilities. We urge further RV follow-up
observations to precisely measure its mass, to enable precise transmission
spectroscopic measurements in the future.
