论文信息 - Two truncated identities of Gauss

Two truncated identities of Gauss

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 pod(n) counting the partitions of n with distinct odd parts. Some further inequalities for variations of partition function are proposed as conjectures.

Jiang Zeng | Victor J. W. Guo | Jiang Zeng

[1] GEORGE E. ANDREWS,et al. Shanks' convergence acceleration transform, Padé approximants and partitions , 1986, J. Comb. Theory, Ser. A.

[2] N. J. A. Sloane,et al. The On-Line Encyclopedia of Integer Sequences , 2003, Electron. J. Comb..

[3] Mircea Merca,et al. Fast Algorithm for Generating Ascending Compositions , 2012, J. Math. Model. Algorithms.

[4] Doron Zeilberger,et al. Bijecting Euler's Partitions-Recurrence , 1985 .

[5] Emil Grosswald,et al. The Theory of Partitions , 1984 .

[6] Daniel Shanks. Two theorems of Gauss , 1958 .

[7] Daniel Shanks,et al. A SHORT PROOF OF AN IDENTITY OF EULER , 1951 .

[8] G. E. Andrews,et al. Truncation of the Rogers–Ramanujan Theta Series , 1983 .

[9] It Informatics. On-Line Encyclopedia of Integer Sequences , 2010 .

[10] George E. Andrews,et al. The fifth and seventh order mock theta functions , 1986 .

[11] G. Hardy,et al. An Introduction to the Theory of Numbers , 1938 .

[12] S. Ole Warnaar. Partial-Sum Analogues of the Rogers - Ramanujan Identities , 2002, J. Comb. Theory, Ser. A.

[13] Robin J. Chapman. Partition identities arising from involutions , 2003, Australas. J Comb..

[14] George E. Andrews,et al. The truncated pentagonal number theorem , 2012, J. Comb. Theory, Ser. A.

[15] James A. Sellers,et al. Arithmetic properties of partitions with odd parts distinct , 2010 .