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In this article, the truncated exponential and Sheffer polynomials are combined to introduce the 2-variable truncated-exponential based Sheffer polynomials (2VTESP) by using operational methods. Examples of certain special polynomials belonging to this family are considered. Operational correspondence between the 2VTESP and Sheffer polynomials is established, which is applied to derive the results for some members belonging to the 2VTESP family.  相似文献
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In this paper, the concepts and the formalism associated with monomiality principle and Sheffer sequences are used to introduce family of Hermite-based Sheffer polynomials. Some properties of Hermite-Sheffer polynomials are considered. Further, an operational formalism providing a correspondence between Sheffer and Hermite-Sheffer polynomials is developed. Furthermore, this correspondence is used to derive several new identities and results for members of Hermite-Sheffer family.  相似文献
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We show that the combination of the formalism underlying the principle of monomiality and of methods of an algebraic nature allows the solution of different families of partial differential equations. Here we use different realizations of the Heisenberg–Weyl algebra and show that a Sheffer type realization leads to the extension of the method to finite difference and integro-differential equations.  相似文献
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An important question in insurance is how to evaluate the probabilities of (non-) ruin of a company over any given horizon of finite length. This paper aims to present some (not all) useful methods that have been proposed so far for computing, or approximating, these probabilities in the case of discrete claim severities. The starting model is the classical compound Poisson risk model with constant premium and independent and identically distributed claim severities. Two generalized versions of the model are then examined. The former incorporates a non-constant premium function and a non-stationary claim process. The latter takes into account a possible interdependence between the successive claim severities. Special attention will be paid to a recursive computational method that enables us to tackle, in a simple and unified way, the different models under consideration. The approach, still relatively little known, relies on the use of remarkable families of polynomials which are of Appell or generalized Appell (Sheffer) types. The case with dependent claim severities will be revisited accordingly.   相似文献
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In this paper, starting from a suitable generating function of a polynomial set, we show how to decide whether the considered polynomial set is d-orthogonal and, if it is so, how to determine the corresponding d-dimensional functional vector. Then, we apply the obtained results to some known and new d-orthogonal polynomial sets. For the known ones, we give new proofs for some already obtained results.  相似文献
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