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EXPLICIT FORMULAS FOR THE FOURIER COEFFICIENTS OF A CLASS OF ETA QUOTIENTS

OLIVIA X. M. YAO

Department of Mathematics, Jiangsu University, Zhenjiang, Jiangsu, 212013, P. R. China

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ERNEST X. W. XIA

Department of Mathematics, Jiangsu University, Zhenjiang, Jiangsu, 212013, P. R. China

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, and

J. JIN

School of Mathematics, Nanjing Normal University, Taizhou College, 225300, Jiangsu, P. R. China

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https://doi.org/10.1142/S179304211250145XCited by:3 (Source: Crossref)

Abstract

Recently, Williams discovered explicit formulas of the coefficients c(n) in the Fourier series expansions of a class of eta quotients. Motivated by the results obtained by Williams, we find that the coefficients c(2n) in the Fourier series expansions of another class of eta quotients can be represented as a linear combination of σ₃(n), σ₃(n/2), σ₃(n/3) and σ₃(n/6). One example is

where

Keywords:

AMSC: 11F20, 11F27

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