The purpose of this note is to provide an alternative proof of two quadratic transformation formulas contiguous to that of Gauss using a differential equation approach.
Meethal, S., Rathie, A. K., & Paris, R. B. (2015). A derivation of two quadratic transformations contiguous to that of Gauss via a differential equation approach. Applied Mathematical Sciences, 9(17), 845-851. https://doi.org/10.12988/ams.2015.4121054