  This article introduces a family of analytical functions of the form x^{\nu}
K_{\nu}(x), where K_{\nu} is the incomplete Bessel function of the third kind.
This family of functions can describe the density profile, projected and
integrated light profiles and the gravitational potentials of galaxies. For the
proper choice of parameters, these functions accurately approximate Sersic
functions over a range of indices and are good fits to galaxy light profiles.
With an additional parameter corresponding to a galaxy core radius, these
functions can fit galaxy like M87 over a factor of 100,000 in radius. Unlike
Sersic profiles, these functions have simple analytical 2-dimensional and
3-dimensional Fourier transforms, so they are easily convolved with spatially
varying point spread function and are well suited for photometric and lensing
analysis. We use these functions to estimate the effects of seeing on lensing
measurements and show that high S/N measurements, even when the PSF is larger
than the galaxy effective radius, should be able to recover accurate estimates
of lensing distortions by weighting light in the outer isophotes that are less
effected by seeing.
