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math.NT2025
An iterative approach toward hypergeometric accelerations
John M. Campbell
Each of Ramanujan's series for is of the form $$ \sum_{n=0}^{\infty} z^n \frac{ (a_{1})_{n} (a_{2})_{n} (a_{3})_{n} }{ (b_{1})_{n} (b_{2})_{n} (b_{3})_{n} } (c_{1} n +…
math.NT2023
Proofs of conjectures on Ramanujan-type series of level 3
John M. Campbell
A Ramanujan-type series satisfies $$ \frac{1}π = \sum_{n=0}^{\infty} \frac{\left( \frac{1}{2} \right)_{n} \left( \frac{1}{s} \right)_{n} \left(1 - \frac{1}{s} \right)_{n} }{ \left(…