Joerg Arndt: Just as quick copy and paste (suggest to start with the last one): J.\ M.\ Borwein, I.\ J.\ Zucker: {Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind}, IMA Journal of Numerical Analysis, vol.12, no.4, pp.519-526, \bdate{1992}.} Greg Martin: {A product of Gamma function values at fractions with the same denominator}, arXiv:0907.4384v1 [math.CA], \bdate{24-July-2009}. URL: \url{http://arxiv.org/abs/0907.4384}.} Albert Nijenhuis: {Small Gamma Products with Simple Values}, arXiv:0907.1689v1 [math.CA], \bdate{9-July-2009}. URL: \url{http://arxiv.org/abs/0907.1689}.} Raimundas Vid\={u}nas: {Expressions for values of the gamma function}, arXiv:math.CA/0403510, \bdate{30-March-2004}. URL: \url{http://arxiv.org/abs/math/0403510}.} ----WDS: Vidunas expresses all the Gamma(p/q) with q=60 or q=24 in terms of algebraic numbers and the Gamma values at just these ten p/q: 1/4, 1/8, 1/3, 1/15, 1/20, 1/24, 1/5, 2/5, 1/60, 7/60. (*) But he then notes that the first 6 among those 10 (i.e the first line) can be expressed in terms of the AGM. He also says all Gamma(p/120) can be expressed in terms of the following six: 1/40, 3/40, 7/40, 1/120, 7/120, 11/120. (**) So... focus your Riesian efforts on the Gamma(p/q) with p/q in the (*) and (**) lines! Vidunas at end also notes that Gamma(1/5) and Gamma(2/5) can be expressed in terms of two hyperelliptic integrals... but is there any fast AGM-like scheme for evaluating them? My earlier mathfun post on this topic was 25 Nov http://mailman.xmission.com/cgi-bin/mailman/private/math-fun/2011-November/0...