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 language | English (US) |
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Pages (from-to) | 767-774 |
Number of pages | 8 |
Journal | International Journal of Number Theory |
Volume | 4 |
Issue number | 5 |
DOIs | |
State | Published - 2008 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory