Infinite and finite series involving central binomial coefficients and closed forms of generalized hypergeometric functions

Ganesh Bahadur Basnet, Narayan Prasad Pahari, Feng Qi +1

Let ${\mathbb{Z}}^{-}=\setminus \{-1,-2,\dots \}$. In 2023, Qi and Lim gave two claims for summing the infinite series $$ \sum_{k=1}^{\infty} \binom{2k}{k} \frac{1}{α+k} \biggl(\frac{\p…