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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
66 Commutation Relations, Normal Ordering, and Stirling Numbers
From the many properties of the partial Bell polynomials (see [280, 935]), we recall the
recurrence relation derived by Bell himself [74, Equation (4.2)],
B
n+1
(y
1
,...,y
n+1
)=
n
k=0
n
k
B
nk
(y
1
,...,y
nk
)y
k+1
. (3.28)
If y
k
= x for all k 1, then this reduces due to (3.27) to Theorem 3.29(5). Furthermore, if
y = y(x) denotes a function of x, and if the derivatives of y with respect to x are denoted
by y
= dy/dx = Dy, y

= Dy
and y
(k)
= Dy
(k1)
,thene
y
D
n
e
y
= B
n
(y, y
,y

,...,y
(n)
);
see [935, Page 35]. Before closing this section, let us mention the recent paper [981], where
some of the above consider ...
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Publisher Resources

ISBN: 9781466579897