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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
260 Commutation Relations, Normal Ordering, and Stirling Numbers
Note that by letting k = n j, (7.73) transforms into a form similar to (7.70),
V
m
U
n
=
n
j=0
m + j 1
j
n!
(n j)!
h
j
U
nj
V
m+j
.
Remark 7.45 Let us point out some history of (7.70) and (7.73). Both formulas have been
rediscovered independently several times. The starting point was the result of Benaoum (see
Proposition 7.42) in particular in its q-deformed version (see Proposition 7.60). Soon after
the publication of [77, 78] Zhang and Wang [1184] derived q-deformed variants of (7.70)
and (7.73). Even earlier, Rosengren [945, Remark 3.5] had derived a q-deformed variant of
(7.70) by specializin ...
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Publisher Resources

ISBN: 9781466579897