Journal of Convex Analysis 25 (2018), No. 1, 065--073
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 Bohr-Mollerup 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 quasi-gamma functions defined in a recent paper by T. Bermúdez, A. Martinón, and K. Sadarangani ["On quasi-gamma functions", Journal of Convex Analysis 21 (2014) 765--783].
Keywords: Bohr-Mollerup theorem, triangular numbers, the gamma function, quasi-convexity.
MSC: 26B25, 33B15; 46E10
[ Fulltext-pdf (203 KB)] for subscribers only.