On gamma quotients and infinite products

Allouche, 1999, The ubiquitous Prouhet–Thue–Morse sequence, 1 Andrews, 1999 Andrews, 2013 Ben-Ari, 2013, On Wallis-type products and Pólyaʼs urn schemes, Amer. Math. Monthly Borwein, 2004 Borwein, 1992, Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind, IMA J. Numer. Anal., 12, 519, 10.1093/imanum/12.4.519 Bouwkamp, 1965, An infinite product, Indag. Math., 27, 40, 10.1016/S1385-7258(65)50004-4 Chamberland, 2013, Multiplicative partitions, Electron. J. Combin., 20, 10.37236/2977 Cohn, 2006, A short proof of the simple continued fraction expansion of e, Amer. Math. Monthly, 113, 57, 10.2307/27641837 Cuyt, 2008 Finch, 2003 Glasser, 2009, Problem 11426, Amer. Math. Monthly, 116, 365 Grimstone, 1980, A product of cosines, Math. Gaz., 64, 120, 10.2307/3615085 Hansen, 1975 Huard, 1995, The Chowla–Selberg formula for genera, Acta Arith., 73, 271, 10.4064/aa-73-3-271-301 Kontsevich, 2001, Periods, 771 Martin Moree, 2000, Approximation of singular series and automata, Manuscripta Math., 101, 385, 10.1007/s002290050222 Nan-Yue, 1995, On the Epstein zeta function, Tamkang J. Math., 26, 165 Nijenhuis, 2010, Short gamma products with simple values, Amer. Math. Monthly, 117, 733, 10.4169/000298910x515802 Paris, 2001 Ramanujan, 1915, On the product ∏n=0∞[1+(xa+nd)3], J. Indian Math. Soc., 7, 209 Robbins, 1979, Solution to E2692: A transcendental function satisfying a duplication formula, Amer. Math. Monthly, 86, 394 Sándor, 1989, A remark on the gamma function, Elem. Math., 44, 73 Selberg, 1967, On Epsteinʼs zeta-function, J. Reine Angew. Math., 227, 86 Singh, 2009, Defining power sums of n and ϕ(n) integers, Int. J. Number Theory, 05, 41, 10.1142/S179304210900189X Sondow, 2010, New Wallis- and Catalan-type infinite products for π,e, and 2+2, Amer. Math. Monthly, 117, 912, 10.4169/000298910x523399 Stephens, 1995, Slowly convergent infinite products, Math. Gaz., 79, 561, 10.2307/3618092 Vidūnas, 2005, Expressions for values of the gamma function, Kyushu J. Math., 59, 267, 10.2206/kyushujm.59.267 Whittaker, 1927 Woods, 1978, Elementary problem E2692, Amer. Math. Monthly, 85, 48 Wright, 1959, Prouhetʼs 1851 solution of the Tarry–Escott problem of 1910, Amer. Math. Monthly, 66, 199, 10.2307/2309513 Zucker, 1977, The evaluation in terms of Γ-functions of the periods of elliptic curves admitting complex multiplication, Math. Proc. Cambridge Philos. Soc., 82, 111, 10.1017/S0305004100053731