<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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/<italic>x</italic>). A new representation of this derivative is given in terms of exponential polynomials.</p></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.

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

Department of Mathematics and Statistics, Ohio Northern University, USA

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

In this note we point out interesting connections among Lah numbers, Laguerre polynomials of order negative one, and exponential polynomials. We also discuss...

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

Published Online: Aug 02, 2016

Page range: 22 - 31

Received: May 04, 2015

DOI: https://doi.org/10.1515/ausm-2016-0002

Keywords
Lah, numbers, Stirling numbers, Laguerre polynomials, exponential polynomials, higher derivatives, binomial identities

© 2016 Khristo N. Boyadzhiev, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Aug 02, 2016

Page range: 22 - 31

Received: May 04, 2015

DOI: https://doi.org/10.1515/ausm-2016-0002

KeywordsLah, numbers, Stirling numbers, Laguerre polynomials, exponential polynomials, higher derivatives, binomial identities

© 2016 Khristo N. Boyadzhiev, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Lah, numbers, Stirling numbers, Laguerre polynomials, exponential polynomials, higher derivatives, binomial identities