Skip to Main Content
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
380 Commutation Relations, Normal Ordering, and Stirling Numbers
Proposition 10.10 Let s = 1 and h =1.Thenth generalized Bell polynomial B
1;1|n
(x)
can be expressed by Hermite polynomials, that is,
B
1;1|n
(x)=
i
x
2
n
H
n
x
i
2
.
In particular, the nth generalized Bell number B
1;1
(n) is given by
B
1;1
(n)=
i
2
n
H
n
1
i
2
.
10.1.2 Exponential Generating Functions
In this section we determine the exponential generating function of the generalized
Touchard polynomials. Recall that the case m = 1 corresponds to the conventional Bell
polynomials, yielding the well-known result
n0
λ
n
n!
T
(1)
n
(x)=
n0
λ
n
n!
B
n
(x)=e
x(e
λ
1)
,
see Theorem 3.29(3). From the definition of ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

The Separable Galois Theory of Commutative Rings, 2nd Edition

The Separable Galois Theory of Commutative Rings, 2nd Edition

Andy R. Magid
Algebraic Operads

Algebraic Operads

Murray R. Bremner, Vladimir Dotsenko
Methods in Algorithmic Analysis

Methods in Algorithmic Analysis

Vladimir A. Dobrushkin
Distributed Computing Through Combinatorial Topology

Distributed Computing Through Combinatorial Topology

Maurice Herlihy, Dmitry Kozlov, Sergio Rajsbaum

Publisher Resources

ISBN: 9781466579897