<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this note, we present an extension of the celebrated Abel– Liouville identity in terms of noncommutative complete Bell polynomials for generalized Wronskians. We also characterize the range equivalence of <italic>n</italic>-dimensional vector-valued functions in the subclass of <italic>n</italic>-times differentiable functions with a nonvanishing Wronskian.</p>
</abstract>

In this note, we present an extension of the celebrated Abel– Liouville identity in terms of noncommutative complete Bell polynomials for generalized Wronskians. We also characterize the range equivalence of n-dimensional vector-valued functions in the subclass of n-times differentiable functions with a nonvanishing Wronskian.

An Extension of the Abel–Liouville Identity

Department of Mathematics, Faculty of Education

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"An Extension of the Abel\u2013Liouville Identity"}

In this note, we present an extension of the celebrated Abel– Liouville identity in terms of noncommutative complete Bell polynomials for generalized...

An Extension of the Abel–Liouville Identity

Published Online: Apr 18, 2022

Page range: 206 - 214

Received: Nov 02, 2021

Accepted: Mar 29, 2022

DOI: https://doi.org/10.2478/amsil-2022-0007

Keywords
Abel–Liouville identity, generalized Wronskians, complete Bell polynomials

© 2022 Zsolt Páles et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

An Extension of the Abel–Liouville Identity

Published Online: Apr 18, 2022

Page range: 206 - 214

Received: Nov 02, 2021

Accepted: Mar 29, 2022

DOI: https://doi.org/10.2478/amsil-2022-0007

KeywordsAbel–Liouville identity, generalized Wronskians, complete Bell polynomials

© 2022 Zsolt Páles et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Abel–Liouville identity, generalized Wronskians, complete Bell polynomials