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Generalized q-Hermite Polynomials
Communications in Mathematical Physics, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Berg, Christian, Ruffing, Andreas
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Nondiagonal Hermite–Sobolev Orthogonal Polynomials
Acta Applicandae Mathematica, 2000Sequences of polynomials \(\{Q_n\}_{n \geq 0}\) orthogonal with respect to the inner product \[ (p,q)_S=\int_{\mathbb R} (p, p') \begin{pmatrix} 1 & \mu \\ \mu & \lambda \end{pmatrix} \begin{pmatrix} q \\ q' \end{pmatrix} e^{-x^2}dx, \quad \lambda -\mu^2>0, \mu \neq 0, \] are studied. First, a relation connecting \(\{Q_n\}\) with Hermite polynomials \(\
Álvarez de Morales, María +3 more
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Improved Hermite multivariate polynomial interpolation
2006 IEEE International Symposium on Information Theory, 2006In this paper we give an algorithm with complexity O(mu2 ) to solve Hermite multivariate polynomial interpolation with mu conditions on its Hasse derivatives. In the case of bivariate interpolation used to perform list-decoding on Reed-Solomon of length n and dimension k with multiplicity m on each point, it permits to obtain a complexity in O(n2m4 ...
Gaborit, Philippe, Ruatta, Olivier
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Combinatorial Applications of Hermite Polynomials
SIAM Journal on Mathematical Analysis, 1982Let $C_1 ,C_2 , \cdots ,C_k $ be k finite sets of elements, where $n_i $ is the number of elements in $C_i (i = 1,2, \cdots ,k)$ and $\sum_{i = 1}^k {n_i } $ is even, $2S$ (say). In any arrangement of the elements into S disjoint pairs, we count the number of homogeneous pairs, i.e., those in which both numbers are from the same subset, $C_i $.
Azor, Ruth, Gillis, J., Victor, J. D.
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Modern Physics Letters A, 1994
The oscillator quantum algebra is extended, through a general approach, in order to put in evidence new q-Hermite polynomials and to discuss the already known ones. Such an approach constraints possible brackets. New sets of corresponding q-bosonic operators are pointed out, reducing for specific values of the subtended parameters to the parabosonic ...
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The oscillator quantum algebra is extended, through a general approach, in order to put in evidence new q-Hermite polynomials and to discuss the already known ones. Such an approach constraints possible brackets. New sets of corresponding q-bosonic operators are pointed out, reducing for specific values of the subtended parameters to the parabosonic ...
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An Identity in Hermite Polynomials
Biometrika, 1971SUMMARY An extension of the Runge (1914) identity in Hermite polynomials is derived, and a test of the assumption of bivariate normality is developed using the identity.
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Some Remarks on Hermite Polynomials
Theory of Probability & Its Applications, 1992See the review Zbl 0731.33007.
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On hermite-bell inverse polynomials
Rendiconti del Circolo Matematico di Palermo, 1984Bell introduced a set of polynomials by \[ \exp g(z)(d^ n/dz^ n)\exp [-g(z)]=Y_ n(g:z)\quad where\quad g(z)=\sum^{\infty}_{n=1}a_ nz^ n. \] In the present paper a related set of polynomials is considered for \(g(z)=pz^{-k}\), where p is a constant and K is a positive integer.
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