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VANISHING COEFFICIENTS IN FOUR QUOTIENTS OF INFINITE PRODUCT EXPANSIONS
Published online by Cambridge University Press: 20 March 2019
Abstract
Motivated by Ramanujan’s continued fraction and the work of Richmond and Szekeres [‘The Taylor coefficients of certain infinite products’, Acta Sci. Math. (Szeged)40(3–4) (1978), 347–369], we investigate vanishing coefficients along arithmetic progressions in four quotients of infinite product expansions and obtain similar results. For example, $a_{1}(5n+4)=0$, where $a_{1}(n)$ is defined by
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- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 100 , Issue 2 , October 2019 , pp. 216 - 224
- Copyright
- © 2019 Australian Mathematical Publishing Association Inc.
Footnotes
This work was supported by the National Natural Science Foundation of China (No. 11501061) and the Fundamental Research Funds for the Central Universities (No. 2018CDXYST0024).
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