Displaying similar documents to “Multidimensional Hermite polynomials of complex Gaussian variables.”

On invariants of random planar endomorphisms

Teimuraz Aliashvili (2003)

Banach Center Publications

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We estimate the expected value of the gradient degree of certain Gaussian random polynomials in two variables and discuss its relations with some other numerical invariants of random polynomials

Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type

Milovanovic, Gradimir V., Cvetkovic, Aleksandar S. (2012)

Mathematica Balkanica New Series

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MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32 In the first part of this survey paper we present a short account on some important properties of orthogonal polynomials on the real line, including computational methods for constructing coefficients in the fundamental three-term recurrence relation for orthogonal polynomials, and mention some basic facts on Gaussian quadrature rules. In the second part we discuss our Mathematica package Orthogonal Polynomials (see [2]) and show...

Some relations satisfied by Hermite-Hermite matrix polynomials

Ayman Shehata, Lalit Mohan Upadhyaya (2017)

Mathematica Bohemica

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The classical Hermite-Hermite matrix polynomials for commutative matrices were first studied by Metwally et al. (2008). Our goal is to derive their basic properties including the orthogonality properties and Rodrigues formula. Furthermore, we define a new polynomial associated with the Hermite-Hermite matrix polynomials and establish the matrix differential equation associated with these polynomials. We give the addition theorems, multiplication theorems and summation formula for the...

Hermite Series with Polar Singularities

Boychev, Georgi S. (2012)

Mathematica Balkanica New Series

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MSC 2010: 33C45, 40G05 Series in Hermite polynomials with poles on the boundaries of their regions of convergence are considered.