English

Explicit expressions for the related numbers of higher order Appell polynomials

Number Theory 2018-06-18 v1

Abstract

In this note, by using the Hasse-Teichm\"uller 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.

Keywords

Cite

@article{arxiv.1806.06023,
  title  = {Explicit expressions for the related numbers of higher order Appell polynomials},
  author = {Su Hu and Takao Komatsu},
  journal= {arXiv preprint arXiv:1806.06023},
  year   = {2018}
}

Comments

14 pages