A complete asymptotic expansion of power means (Q854071)

Let \(x_j>0\), \(w_j\geq 0\) \((j=1,\dots,n)\), \(\sum_{j=1}^n w_j=1\) and \(M_p(\mathbf{x}):= (\sum_{j=1}^n w_j x_j^p)^{1/p}\) for \(p\neq 0\) and \(M_0(\mathbf{x}):= \prod_{j=1}^n x_j^{w_j}.\) The authors' purpose is to give a complete asymptotic expansion of \(M_p({\mathbf x}+{\mathbf a})\) in terms of partial exponential Bell polynomials.