Normalized binomial mid-coefficients and power means Original Research Article

Let imagebe the normalized binomial mid-coefficient and let imagebe the power mean of order t of x,y>0. Furthermore, let k,l≠0 and p,q,r,sgreater-or-equal, slanted0 be integers. We prove: if k=l, then the equationMk(μp,μq)=Ml(μr,μs),only has the solutions (p,q)=(r,s) and (p,q)=(s,r). And, if k≠l, then (0.1) holds if and only if p=q=r=s. This complements a result of Bang and Fuglede, who studied the equation for k=l=0.