Abstract
The linear algebraic theory of the Pascal and Vandermonde matrix is well developed by many authors. In the last two decades many interrelations have been discovered between the mentioned matrices, their generalizations and the Stirling matrices. We follow this direction and discover new matricial relations by using the so-called r-Whitney numbers. Along this way, we develop two natural extensions of the Vandermonde matrix with which we can study and evaluate successive power sums of arithmetic progressions and win new identities for the r-Whitney numbers.
2010 Mathematics Subject Classification::
Acknowledgments
The first author thanks for the invitation to Bogotá where the mayor part of this paper was born.
Funding
The research of István Mező was supported by the Scientific Research Foundation of Nanjing University of Information Science & Technology, and The Startup Foundation for Introducing Talent of NUIST. Project no.: S8113062001. The research of José L. Ramírez was partially supported by Universidad Sergio Arboleda [grant no. DII-262].