Inthispaper,westudythequotientofhypergeometricfunctionsμ_a(r)inthetheoryofRamanujan’sgeneralizedmodularequationfora∈(0,1/2].Severalnewinequalitiesaregivenforthisandrelatedfunctions.Ourmainresultscomplementandgeneralizesomeknownresultsintheliterature.