Extended Bernoulli and Stirling matrices and related combinatorial identities

In this paper we establish plenty of number theoretic and combinatoric identities involving generalized Bernoulli and Stirling numbers of both kinds. These formulas are deduced from Pascal type matrix representations of Bernoulli and Stirling numbers. For this we define and factorize a modified Pascal matrix corresponding to Bernoulli and Stirling cases.Comment: Accepted for publication in Linear Algebra and its Application

On a family of Apostol-Type polynomials

Sean m 2 N, ; ; ; 2 C, a; c 2 R+, y sea Q[m1;] n (x; c; a; ; ; ) la nueva clase de polinomios tipo Apostol generalizados de orden , nivel m y variable x. En el presente trabajo estudiaremos algunas propiedades de esta familia de polinomios y la utilizaremos para demostrar fórmulas de conexión entre éstos polinomios y los polinomios de Apostol Euler y los polinomios de Bernoulli generalizados de nivel m.  Let m 2 N, ; ; ; 2 C, a; c 2 R+ and let Q[m1;] n (x; c; a; ; ; ) be the new class of generalized Apostol-type polynomials of order, m level and variable in x. In the present document we study some properties of these polynomials being used to proof formulas in connection with Apostol-Euler polynomials and generalized Bernoulli polynomilas of m level.