Explicit expressions for the related numbers of higher order Appell polynomials
Abstract
In this note, by using the HasseTeichmüller derivatives, we obtain two explicit expressions for the related numbers of higher order Appell polynomials. One of them presents a determinant expression for the related numbers of higher order Appell polynomials, which involves several determinant expressions of special numbers, such as the higher order generalized hypergeometric Bernoulli and Cauchy numbers, thus recovers the classical determinant expressions of Bernoulli and Cauchy numbers stated in an article by Glaisher in 1875.
 Publication:

arXiv eprints
 Pub Date:
 June 2018
 arXiv:
 arXiv:1806.06023
 Bibcode:
 2018arXiv180606023H
 Keywords:

 Mathematics  Number Theory;
 11B68;
 11B37;
 11C20;
 15A15;
 33C15
 EPrint:
 14 pages