Ramanujan's continued fractions of order $10$ as modular functions

Victor Manuel Aricheta, Russelle Guadalupe

We explore the modularity of the continued fractions $I(\tau ),J(\tau ),T_1(\tau ),T_2(\tau )$ and $U(\tau )=I(\tau )/J(\tau )$ of order $10$, where $I(\tau )$ and $J(\tau )$ are introduced by Rajkhowa and Saikia,…