Hypergeometric Bernoulli polynomials and appell sequences

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Abstract

There are two analytic approaches to Bernoulli polynomials Bn (x): either by way of the generating function zexz/ (ez - 1) = ∑ Bn(x)zn/n! or as an Appell sequence with zero mean. In this article, we discuss a generalization of Bernoulli polynomials defined by the generating function zNexz/(ez - TN-1 (z)), where TN (z) denotes the N th Maclaurin polynomial of ez, and establish an equivalent definition in terms of Appell sequences with zero moments in complete analogy to their classical counterpart. The zero-moment condition is further shown to generalize to Bernoulli polynomials generated by the confluent hypergeometric series.

Original languageEnglish (US)
Pages (from-to)767-774
Number of pages8
JournalInternational Journal of Number Theory
Volume4
Issue number5
DOIs
StatePublished - 2008

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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