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On 5- and 10-dissections for some infinite products

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Quite recently, Xia and Zhao established the 10-dissections for Hirschhorn’s two infinite q-series products by using two MAPLE packages and the theory of modular forms. Utilizing the Jacobi triple product… Click to show full abstract

Quite recently, Xia and Zhao established the 10-dissections for Hirschhorn’s two infinite q-series products by using two MAPLE packages and the theory of modular forms. Utilizing the Jacobi triple product identity, we not only establish the 10-dissections for two infinite q-series products, introduced by Baruah and Kaur, but give an elementary proof of the 10-dissections due to Xia and Zhao. Moreover, we obtain the 5-dissections for four quotients of infinite q-series products related to the Rogers–Ramanujan functions. Using these dissections, the coefficients in these series expansions have periodic sign patterns with a few exceptions.

Keywords: dissections infinite; infinite series; series products; infinite products; series

Journal Title: Ramanujan Journal
Year Published: 2021

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