Astronomy and Astrophysics – Astronomy
Scientific paper
Dec 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999apj...527...86c&link_type=abstract
The Astrophysical Journal, Volume 527, Issue 1, pp. 86-101.
Astronomy and Astrophysics
Astronomy
43
Galaxies: Formation, Galaxies: Structure, Methods: Analytical, Stars: Formation
Scientific paper
We show that an exact expression for the Green's function in cylindrical coordinates is 1/|x-x'| = 1/π√(RR') SUM∞m=-∞ eim(φ - φ')Q(χ) where χ=[R2+R'2+(z- z')2]/(2RR'), and Qm-1/2 is the half-integer degree Legendre function of the second kind. This expression is significantly more compact and easier to evaluate numerically than the more familiar cylindrical Green's function expression, which involves infinite integrals over products of Bessel functions and exponentials. It also contains far fewer terms in its series expansion-and is therefore more amenable to accurate evaluation-than does the familiar expression for |x-x'|-1 that is given in terms of spherical harmonics. This compact Green's function expression is well suited for the solution of potential problems in a wide variety of astrophysical contexts because it adapts readily to extremely flattened (or extremely elongated), isolated mass distributions.
Cohl Howard S.
Tohline Joel E.
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