截断级数系数的渐近性

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation Pub Date : 2025-06-04 DOI:10.1016/j.amc.2025.129592

Renrong Mao

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引用次数: 0

摘要

在Andrews和Merca开创性工作的推动下，截断θ级数近年来得到了广泛的研究。最近，Merca从Jacobi三重积恒等式和五元积恒等式中推测了截断级数中qN系数的非负性。本文利用Wright的圆法，建立了这些级数的系数的渐近公式，并证明了Merca的猜想对于足够大的N是成立的。

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Asymptotics for the coefficients of the truncated theta series

Motivated by the groundbreaking work of Andrews and Merca, truncated theta series are extensively studied in recent years. Recently, Merca made conjectures on the non-negativity of the coefficient of

q^{N}

in truncated series from the Jacobi triple product identity and the quintuple product identity. In this paper, using Wright's Circle Method, we establish asymptotic formulas for the coefficients of these series and prove Merca's conjectures are true for sufficiently large N.

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来源期刊

Applied Mathematics and Computation 数学-应用数学

CiteScore

7.90

自引率

10.00%

发文量

755

审稿时长

36 days

期刊介绍： Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.