منابع مشابه
Counting Words with Laguerre Series
We develop a method for counting words subject to various restrictions by finding a combinatorial interpretation for a product of weighted sums of Laguerre polynomials with parameter α = −1. We describe how such a series can be computed by finding an appropriate ordinary generating function and applying a certain transformation. We use this technique to find the generating function for the numb...
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We show that in the א2-stage countable support iteration of Mathias forcing over a model of CH the complete Boolean algebra generated by absolutely divergent series under eventual dominance is not isomorphic to the completion of P (ω)/fin. This complements Vojtáš’ result, that under cf(c) = p the two algebras are isomorphic [15].
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We give a natural extension of the classical definition of Césaro convergence of a divergent sequence/function. This involves understanding the spectrum of eigenvalues and eigenvectors of a certain Césaro operator on a suitable space of functions or sequences. The essential idea is applicable in identical fashion to other summation methods such as Borel’s. As an example we show how to obtain th...
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Various perturbation series are factorially divergent. The behavior of their high-order terms can be found by Lipatov’s method, according to which they are determined by instanton configurations of appropriate functional integrals. When the Lipatov asymptotics is known and several lowest order terms of the perturbation series are found by direct calculation of diagrams, one can gain insight int...
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The transformation of a Laguerre series f (z) = ∑n=0 λ (α) n L (α) n (z) to a power series f (z) = ∑n=0 γnz n is discussed. Since many nonanalytic functions can be expanded in terms of generalized Laguerre polynomials, success is not guaranteed and such a transformation can easily lead to a mathematically meaningless expansion containing power series coefficients that are infinite in magnitude....
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2000
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-00-05657-4