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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
230 Commutation Relations, Normal Ordering, and Stirling Numbers
obtain a nice limit for q →−1. It is discussed in the spirit of taking the limit q →−1–
in [1002] that the fermionic binomial coefficients are given by
n
k
1
=
0, if n is even and k is odd,
n/2
k/2
, otherwise,
(7.9)
and that the corresponding Galois numbers (see Appendix A) are given by
G
n
(1) = 2
n/2
.
Here we denoted by x the largest integer less than or equal to x and, similarly, by x the
smallest integer larger than or equal to x. Manin and Radul [760] introduced the coefficients
%
n
k
&
1
in a different context as superbinomial coefficients. From recurrence (A.2) of the q-
binomial
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Publisher Resources

ISBN: 9781466579897