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
134 Commutation Relations, Normal Ordering, and Stirling Numbers
Mullen, and Shiue [567]. We will follow their presentation. For any fixed a R,theDickson
polynomial of degree n is defined by
D
n
(x, a)=
n/2
k=0
n
n k
n k
k
(a)
k
x
n2k
,
where xdenotes the greatest integer less than or equal to x. In particular, we define
D
0
(x, a) = 2 for all real x and a. Define the Dickson–Stirling numbers of the first and of
the second kind, denoted D
1
(n, k; a)andD
2
(n, k; a), by
(x a)
n
=
n
k=0
D
1
(n, k; a)(D
k
(x, a) c
k
),
D
n
(x, a) c
n
=
n
k=0
D
2
(n, k; a)(x a)
k
,
for n N
0
,wherec
0
=1andc
k
=0fork 1. Note that for a =0,wehave
D
n
(x, 0) = x
n
, and the Dickson–Stirling numbers ...
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