Operator monotonicity of some functions

We investigate the operator monotonicity of the following functions:f(t)=tγ(tα1−1)(tα2−1)⋯(tαn−1)(tβ1−1)(tβ2−1)⋯(tβn−1)(t∈(0,∞)), where γ∈Rγ∈R and αi,βj>0αi,βj>0 with αi≠βjαi≠βj (i,j=1,2,…,ni,j=1,2,…,n). This property for these functions has been considered by V.E.S. Szabó [14].