论文信息 - Truncated theta series and a problem of Guo and Zeng

Truncated theta series and a problem of Guo and Zeng

We provide partition-theoretic interpretation of two truncated identities of Gauss solving a problem by Guo and Zeng. We also reveal that these results, together with our previous truncation of Euler's pentagonal number theorem, are essentially corollaries of the RogersFine identity. Finally we examine further positivity questions related to the partition function.

George E. Andrews | Mircea Merca | G. Andrews | M. Merca

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

[2] Ae Ja Yee. A truncated Jacobi triple product theorem , 2015, J. Comb. Theory, Ser. A.

[3] Jiang Zeng,et al. Two truncated identities of Gauss , 2012, J. Comb. Theory, Ser. A.

[4] George E. Andrews,et al. Two theorems of Gauss and allied identities proved arithmetically. , 1972 .

[5] Renrong Mao,et al. Proofs of two conjectures on truncated series , 2015, J. Comb. Theory, Ser. A.

[6] L. J. Rogers. On Two Theorems of Combinatory Analysis and Some Allied Identities , 1917 .

[7] G. Andrews. The Theory of Partitions: Frontmatter , 1976 .

[8] Song Heng Chan,et al. Truncated series from the quintuple product identity , 2016 .

[9] Louis W. Kolitsch. Another approach to the Truncated Pentagonal Number Theorem , 2015 .

[10] N. J. Fine,et al. Basic Hypergeometric Series and Applications , 1988 .

[11] Kathy Q. Ji,et al. Bilateral truncated Jacobi's identity , 2016, Eur. J. Comb..