Weisner's method: Difference between revisions

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In [[mathematics]], '''Weisner's method''' is a method for finding [[generating function]]s for [[special functionsfunction]]s using [[representation theory]] of [[Lie groupsgroup]]s and [[Lie algebrasalgebra]]s, introduced by {{harvtxt|Weisner|1955}}. It includes [[TruesdallTruesdell'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|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 | last1last=WeisnerMiller | first1first=LouisWillard Jr.| title=Group-theoretic originReview of certain''Obtaining generatingGenerating functionsFunctions'' |by url=http://projecteuclidElna B.org/euclid.pjm/1172000968 | id={{MR|0086905}} | year=1955McBride | journal=[[PacificCanadian JournalMathematical of MathematicsBulletin]] | issnyear=0030-87301974 | volume=517 | issue=3 | pages=1033–1039447–448| 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]]

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