Title

Computing semi-commuting differential operators in one and multiple variables

Authors

Authors

R. A. Van Gorder

Comments

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Abbreviated Journal Title

Math. Commun.

Keywords

commuting differential operators; semi-commuting operators; locally; commuting operators; Mathematics, Applied; Mathematics

Abstract

We discuss the concept of what we refer to as semi-commuting linear differential operators. Such operators hold commuting operators as a special case. In particular, we discuss a heuristic by which one may construct such operators. Restricting to the case in which one such operator is of degree two, we construct families of linear differential operators semi-commuting with some named operators governing special functions (with a focus on the hypergeometric case, as it holds many other cases as reductions); operators commuting with such special degree two operators will necessarily be contained in these families. In the partial differential operator case, we consider examples in the form of the wave equation with a variable wave speed, and then hypergeometric operators on two variables (such operators define Appell functions).

Journal Title

Mathematical Communications

Volume

19

Issue/Number

2

Publication Date

1-1-2014

Document Type

Article

Language

English

First Page

201

Last Page

219

WOS Identifier

WOS:000345431400001

ISSN

1331-0623

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