A Bohr Mollerup Theorem for Interpolating the Triangular Numbers

Stephen Abbott; Jingyi Wu

Abstract

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].

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

Bohr-Mollerup theorem
triangular numbers
the gamma function
quasi-convexity

Mathematics Subject Classification

26B25, 33B15; 46E10

Suggested citation

S. Abbott, J. Wu. “A Bohr Mollerup Theorem for Interpolating the Triangular Numbers.” Journal of Convex Analysis 25 (2018), No. 1, 65–73.