Rocky Mountain Journal of Mathematics

4-dissections and 8-dissections for some infinite products

Ernest X.W. Xia and X.M. Yao

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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.

Article information

Source
Rocky Mountain J. Math., Volume 44, Number 5 (2014), 1685-1696.

Dates
First available in Project Euclid: 1 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1420071562

Digital Object Identifier
doi:10.1216/RMJ-2014-44-5-1685

Mathematical Reviews number (MathSciNet)
MR3295650

Zentralblatt MATH identifier
1318.11006

Subjects
Primary: 11A55: Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15] 30B70: Continued fractions [See also 11A55, 40A15]

Keywords
$m$-dissection periodicity of sign of coefficients $\theta$ function identit.y

Citation

Xia, Ernest X.W.; Yao, X.M. 4-dissections and 8-dissections for some infinite products. Rocky Mountain J. Math. 44 (2014), no. 5, 1685--1696. doi:10.1216/RMJ-2014-44-5-1685. https://projecteuclid.org/euclid.rmjm/1420071562


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References

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