(1) For a particular mathematical derivation in the field of combustion, I felt it would be more convenient if I can express the weighted Harmonic mean of n variables as an algebraic function or a polynomial in terms of the weights and the variables. It is no problem if it is approximate. Is there such an expression? (weights are all positive and the sum of weights=1).
(2) If such an expression is not possible for constant weights, then is it possible to have a polynomial expression for the expected value and standard deviation of harmonic mean for randomly chosen weights satisfying the sum=1 criteria?
Thanks.
I found a paper that directly addresses the 1st question.
https://www.pnas.org/content/pnas/111/44/15681.full.pdf