Operational Rules and Arbitrary Order Hermite Generating Functions
نویسندگان
چکیده
منابع مشابه
Operational Rules and Arbitrary Order Two-index Two-variable Hermite Matrix Generating Functions
The main aim of this paper is to introduce generalized forms of operational rules associated with operators corresponding to a generalized Hermite matrix polynomials expansions. The associated generating functions is reformulated within the framework of an operational formalism and the theory of exponential operators. We obtain to unilateral and bilateral generating functions by using the same ...
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For use in calculating higher-order coherentand squeezedstate quantities, we derive generalized generating functions for the Hermite polynomials. They are given by ∑∞ n=0 z Hjn+k(x)/(jn + k)!, for arbitrary integers j ≥ 1 and k ≥ 0. Along the way, the sums with the Hermite polynomials replaced by unity are also obtained. We also evaluate the action of the operators exp[a(d/dx)] on well-behaved ...
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We show that the use of operational methods and of multi-index Bessel functions allow the derivation of generating functions, involving the product of an arbitrary number of Laguerre polynomials. ∗2000 Mathematics Subject Classification. 33C45, 44A45. †E-mail:[email protected] ‡E-mail:[email protected] §E-mail:[email protected] ¶E-mail:[email protected] 270 G. Dattol...
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We define a Walsh space which contains all functions whose partial mixed derivatives up to order δ ≥ 1 exist and have finite variation. In particular, for a suitable choice of parameters, this implies that certain reproducing kernel Sobolev spaces are contained in these Walsh spaces. For this Walsh space we then show that quasi-Monte Carlo rules based on digital (t, α, s)-sequences achieve the ...
متن کاملnt - p h / 97 11 01 4 v 1 1 2 N ov 1 99 7 Reply to Comment on “ Generating Functions for Hermite Polynomials of Arbitrary Order ”
The results in the preceding comment are placed on a more general mathematical foundation. In the preceding comment [1], our previous results on arbitrary-order Hermite generating functions [2] were duplicated and extended. This was done by using a power-series expansion of the operator W = exp[−∂/4] to define the Hermite polynomials as Hn(x) = 2 Wx. We observe that this operator definition can...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1998
ISSN: 0022-247X
DOI: 10.1006/jmaa.1998.6080