Weisner's method: Difference between revisions

Revision as of 20:47, 8 June 2022

Latest revision as of 01:20, 13 May 2024

(4 intermediate revisions by 4 users not shown)

Line 1:

{{format footnotes |date=May 2024}}

In [[mathematics]], '''Weisner's method''' is a method for finding [[generating function]]s for [[special function]]s using [[representation theory]] of [[Lie group]]s and [[Lie algebra]]s, introduced by {{harvtxt|Weisner|1955}}. It includes [[Truesdell's method]] as a special case, and is essentially the same as [[Rainville's method]].

{{blockquote|... Weisner's group-theoretic method ... is a technique with uses the differential recurrence relations of a family of special functions to construct a Lie algebra of differential operators (Lie derivatives), under the action of which the family is invariant. The Lie derivatives can be exponentiated to obtain an action of the associated Lie group and this group action yields the generating functions. {{harvtxt|Miller Jr.|1974}}}}

==References==

*{{Citation | last1=McBride | first1=Elna Browning | title=Obtaining generating functions | publisher=[[Springer-Verlag]] | ___location=Berlin, New York | series=Springer Tracts in Natural Philosophy | isbn=978-0-387-05255-7 | mr=0279355 | year=1971 | volume=21 | url-access=registration | url=https://archive.org/details/obtaininggenerat0000mcbr }}

*{{Citation | last=Miller Jr. | first=Willard Jr.| title=Review of ''Obtaining Generating Functions'' by Elna B. McBride | journal=[[Canadian Mathematical Bulletin]] | year=1974 | volume=17 | issue=3 | pages=447–448| url=https://books.google.com/books?id=eCvriuu28BgC&pg=PA448}}

*{{Citation | last1=Weisner | first1=Louis | title=Group-theoretic origin of certain generating functions | url=http://projecteuclid.org/euclid.pjm/1172000968 | mr=0086905 | year=1955 | journal=[[Pacific Journal of Mathematics]] | issn=0030-8730 | volume=5 | issue=6 | pages=1033–1039 | doi=10.2140/pjm.1955.5.1033| doi-access=free }}

[[Category:Generating functions]]

{{math-stub}}