Generalized Bell polynomials
Generalized Bell polynomials
In this paper, generalized Bell polynomials $(\Be_n^\phi)_n$ associated to a sequence of real numbers $\phi=(\phi_i)_{i=1}^\infty$ are introduced. Bell polynomials correspond to $\phi_i=0$, $i\ge 1$. We prove that when $\phi_i\ge 0$, $i\ge 1$: (a) the zeros of the generalized Bell polynomial $\Be_n^\phi$ are simple, real and non positive; (b) the zeros …