Could the Limit be preformed in pieces? (Mathematicians might correct this.)

Here I take the innermost section, take its limit as s-> Infinity, then stick in in

in place of the original counterpart.

In[2]:= Limit[-(2 Gamma[m, ((m*(\[Alpha]/s)^(1/n))/\[CapitalOmega])]),

s -> Infinity,

Assumptions -> {n > 0, m > 0 , 0 < \[Alpha] < s,

M > 0, \[CapitalOmega] > 0}]

Out[2]= -2 Gamma[m]

In[3]:= d=Limit[-(Log[(2-((2 Gamma[m])/Gamma[m]))^M])/Log[s], s->Infinity,

Assumptions->{n>0, m>0 , 0<\[Alpha] <s, \[CapitalOmega]>0}]

Out[3]= Indeterminate

It appears that one ends up with

Log[0] / Log[Infinity]