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Mathematics > Number Theory

Title: Closed form expressions for Appell polynomials

Abstract: We show that any Appell sequence can be written in closed form as a forward difference transformation of the identity. Such transformations are actually multipliers in the abelian group of the Appell polynomials endowed with the operation of binomial convolution. As a consequence, we obtain explicit expressions for higher order convolution identities referring to various kinds of Appell polynomials in terms of the Stirling numbers. Applications of the preceding results to generalized Bernoulli and Apostol-Euler polynomials of real order are discussed in detail.
Comments: 16 pages
Subjects: Number Theory (math.NT)
MSC classes: 11B68, 33C45, 60E05
Cite as: arXiv:1803.05943 [math.NT]
  (or arXiv:1803.05943v1 [math.NT] for this version)

Submission history

From: Jose Adell A. [view email]
[v1] Thu, 15 Mar 2018 18:45:27 GMT (12kb)