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

Abstract

Abstract.Motivated by time series analysis, we consider the problem of solving the recurrence relation u n+1 = v n+1 + u n ⊗ v n for n = 0 and u n , given the sequence v n . A solution is given as a Bell polynomial. When v n can be written as a weighted sum of nth powers, then the solution u n also takes this form.Mathematical subject classification: 33E99.