Lah numbers and Laguerre polynomials of order negative one
Khristo N. Boyadzhiev (Department of Mathematics, Statistics, Ohio, Northern University, Ada, OH)
TL;DR
This paper explores the relationships between Lah numbers, negative order Laguerre polynomials, and exponential polynomials, providing new formulas for derivatives of exp(1/x) using exponential polynomials.
Contribution
It introduces novel connections among special number sequences and polynomials, and presents a new representation for higher derivatives of exp(1/x).
Findings
Connections among Lah numbers, Laguerre polynomials, and exponential polynomials.
New formulas for derivatives of exp(1/x).
Representation of derivatives in terms of exponential polynomials.
Abstract
In this article we point out interesting connections among Lah numbers, Laguerre polynomials of order negative one, and exponential polynomials. We also discuss several different expressions for the higher order derivatives of exp (1/x). A new representation of these derivatives is given in terms of exponential polynomials
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Mathematical functions and polynomials