3 papers
math.CA2026
A further q-analogue of Gosper's strange series
John M. Campbell, Yuka Yamaguchi
Recently, the second author [Ramanujan J. 2026] introduced and proved a -series identity that appears to provide the first known -analogue of an evaluation for a ${}_{2}F_{1}…
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(…