4-dissections and 8-dissections for some infinite products

Ernest X.W. Xia; X.M. Yao

doi:10.1216/RMJ-2014-44-5-1685

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2014 4-dissections and 8-dissections for some infinite products

Ernest X.W. Xia, X.M. Yao

Rocky Mountain J. Math. 44(5): 1685-1696 (2014). DOI: 10.1216/RMJ-2014-44-5-1685

Abstract

In this paper, we establish 4- and 8-dissections for some infinite products. In particular, we generalize Hirschhorn's formulas for 8-dissections of a continued fraction of Gordon and its reciprocal. Our results also imply a theorem on the periodicity of signs of the coefficients of an infinite product given by Chan and Yesilyurt.

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Ernest X.W. Xia. X.M. Yao. "4-dissections and 8-dissections for some infinite products." Rocky Mountain J. Math. 44 (5) 1685 - 1696, 2014. https://doi.org/10.1216/RMJ-2014-44-5-1685