Tables of the Generalized Stirling Numbers of the First Kind

Two doubly indexed families of homogeneous and isobaric polynomials in several indeterminates are considered: the (partial) exponential Bell polynomials B n , k and a new family S n , k Z X 1 , , X n - k + 1 such that X 1 - ( 2 n - 1 ) S n , k and B n , ...

Generalizing recent results of Egge and Mongelli, we show that each diagonal sequence of the Jacobi-Stirling numbers Jc(n,k;z) and JS(n,k;z) is a Polya frequency sequence if and only if z@?[-1,1] and study the z-total positivity properties of these ...

In the paper, the authors elementarily unify and generalize eight identities involving the functions +/-1e^+/-^t-1 and their derivatives. By one of these identities, the authors establish two explicit formulae for computing Euler polynomials and two-...