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We measure the HI mass function (HIMF) and velocity width function (WF)across environments over a range of masses $7.2<\log(M_{HI}/M_{\odot})<10.8$,and profile widths $1.3\log(km/s)<\log(W)<2.9\log(km/s)$, using a catalog of~7,300 HI-selected galaxies from the ALFALFA Survey, located in the region ofsky where ALFALFA and SDSS (Data Release 7) North overlap. We divide our galaxysample into those that reside in large-scale voids (void galaxies) and thosethat live in denser regions (wall galaxies). We find the void HIMF to be wellfit by a Schechter function with normalization$\Phi^*=(1.37\pm0.1)\times10^{-2} h^3Mpc^{-3}$, characteristic mass$\log(M^*/M_{\odot})+2\log h_{70}=9.86\pm0.02$, and low-mass-end slope$\alpha=-1.29\pm0.02$. Similarly, for wall galaxies, we find best-fittingparameters $\Phi^*=(1.82\pm0.03)\times10^{-2} h^3Mpc^{-3}$,$\log(M^*/M_{\odot})+2\log h_{70}=10.00\pm0.01$, and $\alpha=-1.35\pm0.01$. Weconclude that void galaxies typically have slightly lower HI masses than theirnon-void counterparts, which is in agreement with the dark matter halo massfunction shift in voids assuming a simple relationship between DM mass and HImass. We also find that the low-mass slope of the void HIMF is similar to thatof the wall HIMF suggesting that there is either no excess of low-mass galaxiesin voids or there is an abundance of intermediate HI mass galaxies. We fit amodified Schechter function to the ALFALFA void WF and determine itsbest-fitting parameters to be $\Phi^*=0.21\pm0.1 h^3Mpc^{-3}$,$\log(W^*)=2.13\pm0.3$, $\alpha=0.52\pm0.5$ and high-width slope$\beta=1.3\pm0.4$. For wall galaxies, the WF parameters are:$\Phi^*=0.022\pm0.009 h^3Mpc^{-3}$, $\log(W^*)=2.62\pm0.5$,$\alpha=-0.64\pm0.2$ and $\beta=3.58\pm1.5$. Because of large uncertainties onthe void and wall width functions, we cannot conclude whether the WF isdependent on the environment.

The HI Mass Function and Velocity Width Function of Void Galaxies in the Arecibo Legacy Fast ALFA Survey