Log Riemann Zeta plus Zipf distribution

From @bob-carpenter on February 12, 2014 18:9

It'd be nice to have the Zipf distribution in Stan:

See: http://mathworld.wolfram.com/ZipfDistribution.html

The pmf is involves the Riemann zeta function, which is available from Boost:

http://www.boost.org/doc/libs/1_55_0/libs/math/doc/html/math_toolkit/zetas/zeta.html

so we could add it directly with auto-diff. But auto-diffing these numerical
approximations to functions isn't ideal.

Plus, we really need log_zeta for Stan, and then we'd want a direct scheme
for evaluating both

log(zeta(s)

and

  d/ds log(zeta(s)) = 1/zeta(s) d/ds zeta(s).

See also, this paper by Choudhury (1995), which is what the Mathworld page cites: https://www.jstor.org/stable/52768?seq=1#page_scan_tab_contents

Copied from original issue: stan-dev/stan#551

No source file, test, or entry point is named. Begin with the MathWorld Zipf description, Boost's zeta documentation, and the cited Choudhury paper; the issue is done when Stan has a suitable log_zeta and Zipf distribution with automatic differentiation support.