A Bohr Mollerup Theorem for Interpolating the Triangular Numbers

作者：Abbott Stephen^*; Wu Jingyi

来源：Journal of Convex Analysis, 2018, 25(1): 65-73.

• Bohr-Mollerup Theorem
• triangular numbers
• gamma function
• quasi-convexity

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 Bermudez, Martinon and Sadarangani (2014).

• 出版日期2018