4-dissections and 8-dissections for some infinite products. (English) Zbl 1318.11006

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

Rocky Mt. J. Math. 44, No. 5, 1685-1696 (2014).

Summary: In this paper, we establish 4- and 8-dissections for some infinite products. In particular, we generalize M. D. Hirschhorn’s formulas for 8-dissections of a continued fraction of Gordon and its reciprocal [Ramanujan J. 5, No. 4, 369–375 (2001; Zbl 0993.30003)]. Our results also imply a theorem on the periodicity of signs of the coefficients of an infinite product given by S. H. Chan and H. Yesilyurt [Pac. J. Math. 225, No. 1, 13–32 (2006; Zbl 1118.30002)].

MSC:

11A55	Continued fractions
30B70	Continued fractions; complex-analytic aspects

Keywords:

\(m\)-dissection; periodicity of sign of coefficients; theta function identity

Citations:

Zbl 0993.30003; Zbl 1118.30002

References:

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