Investigation reveals connections between continued fractions and their reciprocal, suggesting new partition identities.
In the present article, we obtain thirteen special cases of Ramanujan's continued fraction and establish $2$-, $4$-dissections of those continued fractions. Also, we derive algebraic relations connecting continued fractions with their respective reciprocals and we validate our results establishing the coloured partition identities.
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Bhat et al. (2026) studied this question.
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