Open Access
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.

Citation

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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

Information

Published: 2014
First available in Project Euclid: 1 January 2015

zbMATH: 1318.11006
MathSciNet: MR3295650
Digital Object Identifier: 10.1216/RMJ-2014-44-5-1685

Subjects:
Primary: 11A55 , 30B70

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

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

Vol.44 • No. 5 • 2014
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