A class of complete potential-density basis sets in cylindrical (R, φ, z) coordinates is presented. This class is suitable for stability studies of galactic disks in three dimensions and includes basis sets tailored for disks with vertical density profiles that are exponential (e~(-∣z∣/z_0)), Gaussian [e~(-(∣z∣/z_0)~2)], or locally isothermal [sech~2 (z/z_0)]. The basis sets are nondiscrete and nonbiorthogonal; however, the extra numerical computations required (compared with discrete biorthogonal sets) are explained and constitute a small overhead. The method of construction is simple and can be used to construct basis sets for other density distributions that are best described in circular or elliptic cylindrical coordinates. Proving completeness is also straightforward. When combined with a basis set designed for spheroidal systems, the basis sets presented here can be used to study the stability of realistic disks embedded in massive halos.
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