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Discussion on some conjectures regarding the periodicity of sign patterns of certain infinite products involving the Rogers-Ramanujan Continued Fractions by Ghoshal, Suparno; Jana, Arijit is a scholarly article available to read on EtoBox.

What is Discussion on some conjectures regarding the periodicity of sign patterns of certain infinite products involving the Rogers-Ramanujan Continued Fractions about?

Let $R(q)$ denote the Rogers-Ramanujan continued fraction. Define $$ \frac{1}{R^5(q)}=\displaystyle \sum_{n=0}^{\infty}A(n)q^{n} \quad \text{and} \quad R^5(q)=\displaystyle\sum_{n=0}^{\infty}B(n)q^{n}.$$ Baruah and Sarma recently posed conjectures regarding the sign patterns of $A(5n), B(5n)$ for $n\geq 0.$ In this paper, we show that these conjectures do not hold for $n=0$.

Author

Ghoshal, Suparno; Jana, Arijit

Published

2025

Language

EN