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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
A Generalization of the Weyl Algebra 337
Remark 8.145 In the proof of Proposition 8.144 we used the structure of higher derivatives
of f
/f. In [607] (see also [38]) combinatorial aspects of higher derivatives of inverses 1/f
were considered. More recently, Jakimczuk [590] considered higher derivatives of arbitrary
fractions h/f .
Combining (8.81) and Proposition 8.144, we conclude that Be
s;h
satisfies an algebraic
differential equation, provided Se
s;h
satisfies an algebraic differential equation.
Lemma 8.146 Let h C \{0}.ThenSe
s;h
satisfies for all s R the algebraic differential
equation
Se

s;h
Se
s;h
(s +1)(Se

s;h
)
2
=0. (8.134)
In the particular case ...
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Publisher Resources

ISBN: 9781466579897