منابع مشابه
On Hermite-hermite Matrix Polynomials
In this paper the definition of Hermite-Hermite matrix polynomials is introduced starting from the Hermite matrix polynomials. An explicit representation, a matrix recurrence relation for the Hermite-Hermite matrix polynomials are given and differential equations satisfied by them is presented. A new expansion of the matrix exponential for a wide class of matrices in terms of Hermite-Hermite ma...
متن کاملGeneralized Hermite Polynomials 1
The new method for obtaining a variety of extensions of Hermite polynomials is given. As a first example a family of orthogonal polynomial systems which includes the generalized Hermite polynomials is considered. Apparently, either these polynomials satisfy the differential equation of the second order obtained in this work or there is no differential equation of a finite order for these polyno...
متن کاملGeneralized numerical ranges of matrix polynomials
In this paper, we introduce the notions of C-numerical range and C-spectrum of matrix polynomials. Some algebraic and geometrical properties are investigated. We also study the relationship between the C-numerical range of a matrix polynomial and the joint C-numerical range of its coefficients.
متن کاملAsymptotic analysis of generalized Hermite polynomials
We analyze the polynomials H n(x) considered by Gould and Hopper, which generalize the classical Hermite polynomials. We present the main properties of H n(x) and derive asymptotic approximations for large values of n from their differential-difference equation, using a discrete ray method. We give numerical examples showing the accuracy of our formulas.
متن کاملOn linearization and connection coefficients for generalized Hermite polynomials
We consider the problem of finding explicit formulae, recurrence relations and sign properties for both connection and linearization coefficients for generalized Hermite polynomials. The most computations are carried out by the computer algebra system Maple using appropriate algorithms.
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ژورنال
عنوان ژورنال: The Electronic Journal of Linear Algebra
سال: 2003
ISSN: 1081-3810
DOI: 10.13001/1081-3810.1113