The estimation of the zeros of the Bell and r-Bell polynomials

It is a classical result that the zeros of the Bell polynomials are real and negative. In this study we deal with the asymptotic growth of the leftmost zeros of the Bell polynomials and generalize the results for the r-Bell polynomials, too. In addition, we offer a heuristic approach for the approximation of the maximizing index of the Stirling numbers of both kind.