Two truncated identities of Gauss

Abstract

Two new expansions for partial sums of Gauss' triangular and square numbers series are given. As a consequence, we derive a family of inequalities for the overpartition function p(n) and for the partition function p1(n) counting the partitions of n with distinct odd parts. Some further inequalities for variations of partition function are proposed as conjectures.

0

Turn this paper into a lesson

ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.

Discussion (0)

Sign in to join the discussion.

Loading comments…