Series with Hermite polynomials and applications
نویسندگان
چکیده
منابع مشابه
Some applications of the Hermite matrix polynomials series expansions 1
This paper deals with Hermite matrix polynomials expansions of some relevant matrix functions appearing in the solution of di erential systems. Properties of Hermite matrix polynomials such as the three terms recurrence formula permit an e cient computation of matrix functions avoiding important computational drawbacks of other well-known methods. Results are applied to compute accurate approxi...
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In this paper, a new and efficient approach is applied for numerical approximation of the linear differential equations with variable coeffcients based on operational matrices with respect to Hermite polynomials. Explicit formulae which express the Hermite expansion coeffcients for the moments of derivatives of any differentiable function in terms of the original expansion coefficients of the f...
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The cycle index polynomial of a symmetric group is a basic tool in combinatorics and especially in Pólya enumeration theory. It seems irrelevant to numerical analysis. Through Faá di Bruno’s formula, cycle index is connected with numerical analysis. In this work, the Hermite interpolation polynomial is explicitly expressed in terms of cycle index. Applications in Gauss-Turán quadrature formula ...
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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 کاملoperational matrices with respect to hermite polynomials and their applications in solving linear di erential equations with variable coecients
in this paper, a new and ecient approach is applied for numerical approximationof the linear di erential equations with variable coecients based on operational matriceswith respect to hermite polynomials. explicit formulae which express the hermite expansioncoecients for the moments of derivatives of any di erentiable function in terms of theoriginal expansion coecients of the function itse...
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ژورنال
عنوان ژورنال: Publicationes Mathematicae Debrecen
سال: 2012
ISSN: 0033-3883
DOI: 10.5486/pmd.2012.5072