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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
312 Commutation Relations, Normal Ordering, and Stirling Numbers
Example 8.91 Let s =2and h =1. From Corollary 8.88, we obtain for the exponential
generating function of the generalized Bell numbers that
Be
2,1
(x)=e
1
12x
, (8.73)
and from Corollary 8.90 that the generalized Bell numbers are given by
B
2;1
(n)=e
j0
(1)
nj
j
n
j!
n1
k=0
1
2k
j
.
Example 8.92 Let s = 1 and h =1. From Corollary 8.88, we obtain for the exponential
generating function of the generalized Bell numbers that
Be
1,1
(x)=e
x+
1
2
x
2
, (8.74)
and from Corollary 8.89 that the generalized Bell numbers are given by
B
1;1
(n)=
1
e
j0
(2j)
n
j!2
j
.
Relation (8.74) shows that B
1;1
(n) equals the tot
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Publisher Resources

ISBN: 9781466579897