Abstract
In this paper, we derive four continued fractions of order 32 as special cases of a general continued fraction identity recorded by Ramanujan. We prove theta-function representations and establish a modular relation connecting the four continued fractions. We also prove 2-, 4-, 8-, and 16-dissections for a continued fraction and show that the sign of the coefficients in the power series expansion of a continued fraction and its reciprocal are periodic with period 32. The results are analogous to those of the famous Rogers-Ramanujan continued fraction.
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Chetry, J., Saikia, N. Modular identities and dissections of continued fractions of order thirty-two. São Paulo J. Math. Sci. 17, 701–719 (2023). https://doi.org/10.1007/s40863-021-00253-0
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DOI: https://doi.org/10.1007/s40863-021-00253-0