Two formulae of Gauss and Bailey for $_2F_1 (\frac12)$-series
Volume 128 / 2022
Annales Polonici Mathematici 128 (2022), 113-120
MSC: Primary 33C20; Secondary 33D15.
DOI: 10.4064/ap210715-15-12
Published online: 21 March 2022
Abstract
As a common extension of the second Gauss theorem and Bailey’s summation formula for $_2F_1\big(\frac 12\big)$-series, a transformation formula containing three free parameters is derived. The corresponding $q$-series counterpart is also established.
