Hypergeometric accelerations with shifted indices
John Maxwell Campbell · The Journal of Difference Equations and Applications · 2025
We apply a variant of an acceleration method due to Wilf using what we refer to as shifted indices for Pochhammer symbols involved in our first-order, inhomogeneous, holonomic difference equations derived via Zeilberger’s algorithm, to build upon the work of Chu and Zhang on series accelerations obtained via the modified Abel lemma on summation by parts. We recover many of Chu and Zhang’s accelerated series and we introduce many inequivalent series for universal constants, including series of Ramanujan type involving linear polynomials as summand factors, as in Ramanujan’s series for 1π.