2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68283This paper presents a family of new integral representations and asymptotic series of the multiple gamma function. The numerical schemes for high-precision computation of the Barnes gamma function and Glaisher's constant are also discussed.18 pages, AMS-LATEXClassical Analysis and ODEsMathematical Physics33E20, 11M35text