
Journal of Convex Analysis 25 (2018), No. 1, 065073 Copyright Heldermann Verlag 2018 A Bohr Mollerup Theorem for Interpolating the Triangular Numbers Stephen Abbott Dept. of Mathematics, Middlebury College, 303 College Street, Middlebury, VT 05753, U.S.A. abbott@middlebury.edu Jingyi Wu Dept. of Mathematics, Middlebury College, 303 College Street, Middlebury, VT 05753, U.S.A. jw@middlebury.edu The BohrMollerup Theorem (1922) provides an elegant criterion under which the gamma function is the unique function interpolating n!. We prove an analogous uniqueness theorem for interpolating the triangular numbers that, like the original, is grounded in the theory of convex functions. We then explore parallels with the class of quasigamma functions defined in a recent paper by T. Bermúdez, A. Martinón, and K. Sadarangani ["On quasigamma functions", Journal of Convex Analysis 21 (2014) 765783]. Keywords: BohrMollerup theorem, triangular numbers, the gamma function, quasiconvexity. MSC: 26B25, 33B15; 46E10 [ Fulltextpdf (203 KB)] for subscribers only. 