An iterative approach toward hypergeometric accelerations

John M. Campbell

Each of Ramanujan's series for $\frac{1}{\pi }$ is of the form $$ \sum_{n=0}^{\infty} z^n \frac{ (a_{1})_{n} (a_{2})_{n} (a_{3})_{n} }{ (b_{1})_{n} (b_{2})_{n} (b_{3})_{n} } (c_{1} n +…