# [Calculation 18] Some Useful Formulas from the Jacobi Triple Product

In this post, we introduce some useful formulas, which can be proved by the Jacobi Triple Product [2]. As before, we always denote $f$ as the Ramanujan Theta Function, which is defined in [3].   Corollary. If $|q|<1$ then, \begin{align*} … Continue reading

# [Calculation 15] Introduction to the Ramanujan Theta Functions

In this post, we introduce the Ramanujan theta functions $f(a,b)$, which generalize the form of the Jacobi theta functions. Here we define the Ramanujan theta function, and introduce some elementary properties. First, we define the Ramanujan theta function as  … Continue reading