Lah numbers, Laguerre polynomials of order negative one, and the nth derivative of exp(1/x)

Khristo N. Boyadzhiev

doi:10.1515/ausm-2016-0002

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Lah numbers, Laguerre polynomials of order negative one, and the nth derivative of exp(1/x)

Acta Universitatis Sapientiae, Mathematica

Volume 8 (2016): Issue 1 (August 2016)

By: Khristo N. Boyadzhiev

Open Access

|Aug 2016

Abstract

In this note 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 nth derivative of exp(1/x). A new representation of this derivative is given in terms of exponential polynomials.

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Articles in this issue

DOI: https://doi.org/10.1515/ausm-2016-0002 | Journal eISSN: 2066-7752

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Language: English

Page range: 22 - 31

Submitted on: May 4, 2015

Published online: Aug 2, 2016

Published in print: Aug 1, 2016

Published by: Sapientia Hungarian University of Transylvania

In partnership with: Paradigm Publishing Services

Keywords:

Lah,

numbers,

Stirling numbers,

Laguerre polynomials,

exponential polynomials,

higher derivatives,

binomial identities

MSC:

11M06,

33B15

Related subjects:

Mathematics,

General mathematics

© 2016 Khristo N. Boyadzhiev, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 8 (2016): Issue 1 (August 2016)