Solutions to the recurrence relation u n+1 = v n+1 + u n ？ v n in terms of Bell polynomials

motivated by time series analysis, we consider the problem of solving the recurrence relation un+1 = vn+1 +un？vn for n ≠ 0 and un, given the sequence vn. a solution is given as a bell polynomial. when vn can be written as a weighted sum of nth powers, then the solution un also takes this form. mathematical subject classification: 33e99.