Results 21 to 30 of about 33,621 (261)
On squares of Hermite polynomials [PDF]
Aequationes Mathematicae, 1983 In this interesting paper, the authors have obtained a new integral representation for the squares of Hermite polynomials. It is further used to obtain the following asymptotic expansion \[ \bar e^{x^ 2}[H_ n(x)]^ 2/2^ nn!=(1/\sqrt{2})\sum^{\infty}_{r=0}(a_ r/\Gamma (- r+)n^{r+})+ \] \[ +((-1)^ n/\sqrt{2})\sum^{\infty}_{r=0}b_ r(x\sqrt{2/n})^{r+}J_{-p-}
Glasser, M.L., Shawagfeh, Nabil
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Zeros of exceptional Hermite polynomials [PDF]
Journal of Approximation Theory, 2015 We study the zeros of exceptional Hermite polynomials associated with an even partition $λ$. We prove several conjectures regarding the asymptotic behavior of both the regular (real) and the exceptional (complex) zeros. The real zeros are distributed as the zeros of usual Hermite polynomials and, after contracting by a factor $\sqrt{2n}$, we prove that
Kuijlaars, Arno, Milson, Robert
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Coefficients of Wronskian Hermite polynomials [PDF]
Studies in Applied Mathematics, 2020 AbstractWe study Wronskians of Hermite polynomials labeled by partitions and use the combinatorial concepts of cores and quotients to derive explicit expressions for their coefficients. These coefficients can be expressed in terms of the characters of irreducible representations of the symmetric group, and also in terms of hook lengths.
Niels Bonneux +2 more
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AIMS Mathematics, 2023 In this study, we develop various features in special polynomials using the principle of monomiality, operational formalism, and other qualities. By utilizing the monomiality principle, new outcomes can be achieved while staying consistent with past ...
Mohra Zayed, Shahid Wani
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The Expansion of Wronskian Hermite Polynomials in the Hermite Basis [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2021 We express Wronskian Hermite polynomials in the Hermite basis and obtain an explicit formula for the coefficients. From this we deduce an upper bound for the modulus of the roots in the case of partitions of length 2. We also derive a general upper bound for the modulus of the real and purely imaginary roots.
Codruţ Grosu, Corina Grosu
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Survey of Hermite Interpolating Polynomials for the Solution of Differential Equations
Mathematics, 2023 With progress on both the theoretical and the computational fronts, the use of Hermite interpolation for mathematical modeling has become an established tool in applied science.
Archna Kumari, Vijay K. Kukreja
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Generalized Burchnall-Type Identities for Orthogonal Polynomials and Expansions [PDF]
, 2018 Burchnall's method to invert the Feldheim-Watson linearization formula for the Hermite polynomials is extended to all polynomial families in the Askey-scheme and its $q$-analogue.
Ismail, Mourad E. H. +2 more
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Identities involving 3-variable Hermite polynomials arising from umbral method
Advances in Difference Equations, 2020 In this paper, we employ an umbral method to reformulate the 3-variable Hermite polynomials and introduce the 4-parameter 3-variable Hermite polynomials. We also obtain some new properties for these polynomials. Moreover, some special cases are discussed
Nusrat Raza +3 more
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Orthogonality of Hermite polynomials in superspace and Mehler type formulae [PDF]
, 2011 In this paper, Hermite polynomials related to quantum systems with orthogonal O(m)-symmetry, finite reflection group symmetry G < O(m), symplectic symmetry Sp(2n) and superspace symmetry O(m) x Sp(2n) are considered.
Coulembier, Kevin +2 more
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