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Commutation Relations, Normal Ordering, and Stirling Numbers
book

Commutation Relations, Normal Ordering, and Stirling Numbers

by Toufik Mansour, Matthias Schork
September 2015
Intermediate to advanced content levelIntermediate to advanced
528 pages
19h 34m
English
Chapman and Hall/CRC
Content preview from Commutation Relations, Normal Ordering, and Stirling Numbers
The q-Deformed Weyl Algebra and the Meromorphic Weyl Algebra 265
Comparing this with (7.83), we obtain A
kn
= Sm
1
(n, k). By (8.71), we obtain the first
explicit expression for the meromorphic Stirling numbers,
Sm
h
(n, k)=
h
2
nk
n
n k
(n 1)!
(k 1)!
.
Comparing (7.84) with the definition of Lang’s generalized Stirling numbers S(r; n, k)in
[710] reveals that Sm
1
(n, k)=|S(1; n, k)|, and the latter count unordered k-forests of
ordered rooted increasing trees with vertices of any out-degree where there are n vertices
altogether [712]; see also A132026 in [1019]. Another interpretation can be found by recalling
Theorem 7.48, thereby identifying Sm
h
(n,
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Publisher Resources

ISBN: 9781466579897