Skip to Main content Skip to Navigation
Journal articles

Truncated Series with Nonnegative Coefficients from the Jacobi Triple Product

Abstract : Andrews and Merca investigated a truncated version of Euler's pentagonal number theorem and showed that the coefficients of the truncated series are nonnegative. They also considered the truncated series arising from Jacobi's triple product identity, and they conjectured that its coefficients are nonnegative. This conjecture was posed by Guo and Zeng independently and confirmed by Mao and Yee using different approaches. In this paper, we provide a new combinatorial proof of their nonnegativity result related to Euler's pentagonal number theorem. Meanwhile, we find an analogous result for a truncated series arising from Jacobi's triple product identity in a different manner.
Document type :
Journal articles
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-03498175
Contributor : Srinivas Kotyada Connect in order to contact the contributor
Submitted on : Monday, December 20, 2021 - 8:41:06 PM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM

File

44Article05.pdf
Publisher files allowed on an open archive

Identifiers

Collections

Citation

Liuquan Wang. Truncated Series with Nonnegative Coefficients from the Jacobi Triple Product. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2022, Special Commemorative volume in honour of Srinivasa Ramanujan - 2021, Volume 44 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2021, pp.51 -- 60. ⟨10.46298/hrj.2022.8931⟩. ⟨hal-03498175⟩

Share

Metrics

Record views

7

Files downloads

79