Results 11 to 20 of about 14,680 (235)

Doubling (Dual) Hahn Polynomials: Classification and Applications [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2016
We classify all pairs of recurrence relations in which two Hahn or dual Hahn polynomials with different parameters appear. Such couples are referred to as (dual) Hahn doubles.
Oste, Roy, Van der Jeugt, Joris
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Building some symmetric Laguerre-Hahn functionals of class two at most through the sum of symmetric functionals as pseudofunctions with a Dirac measure at origin

International Journal of Mathematics and Mathematical Sciences, 2006
We show that if v is a symmetric regular Laguerre-Hahn linear form (functional), then the linear form u defined by u=−λx−2v+δ0 is also regular and symmetric Laguerre-Hahn linear form for every complex λ except for a discrete set of numbers depending ...
M. Sghaier, J. Alaya
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Two $q$-operational equations and Hahn polynomials [PDF]

Complex Analysis and Operator Theory, 2022
Motivated by Liu's recent work in \cite{Liu2022}. We shall reveal the essential feature of Hahn polynomials by presenting two new $q$-exponential operators. These lead us to use a systematic method to study identities involving Hahn polynomials. As applications, we use the method of $q$-exponential operator to prove the bilinear generating function of ...
Gu Jing, Yang DunKun, Qi Bao
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Multivariable continuous Hahn polynomials [PDF]

Journal of Mathematical Physics, 1988
A multivariable generalization of the continuous Hahn polynomials is presented; it is a (4p+4)-parameter family, where p is the number of variables. It is shown that they are orthogonal with respect to subspaces of equal degree and biorthogonal within a given subspace. In the simplest case the multivariable weight function takes the form sech[π(x1+x2+⋅⋅
M. V. Tratnik
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Hahn polynomials and the Burnside process [PDF]

The Ramanujan Journal, 2021
We study a natural Markov chain on $\{0,1,\cdots,n\}$ with eigenvectors the Hahn polynomials. This explicit diagonalization makes it possible to get sharp rates of convergence to stationarity. The process, the Burnside process, is a special case of the celebrated `Swendsen-Wang' or `data augmentation' algorithm.
Persi Diaconis, Chenyang Zhong
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Spectral accuracy for the Hahn polynomials [PDF]

, 2016
We consider in this paper the Hahn polynomials and their application in numerical methods. The Hahn polynomials are classical discrete orthogonal polynomials. We analyse the behaviour of these polynomials in the context of spectral approximation of partial differential equations.
René Goertz, Philipp Öffner
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Integrable differential systems for deformed Laguerre–Hahn orthogonal polynomials [PDF]

Nonlinearity, 2023
AbstractOur work studies sequences of orthogonal polynomials{Pn(x)}n⩾0of the Laguerre–Hahn class, whose Stieltjes functions satisfy a Riccati type differential equation with polynomial coefficients, which are subject to a deformation parametert. We derive systems of differential equations and give Lax pairs, yielding nonlinear differential equations ...
M.N. Rebocho, N. S. Witte
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Dual $-1$ Hahn polynomials: “Classical” polynomials beyond the Leonard duality [PDF]

Proceedings of the American Mathematical Society, 2012
We introduce the -1 dual Hahn polynomials through an appropriate $q \to -1$ limit of the dual q-Hahn polynomials. These polynomials are orthogonal on a finite set of discrete points on the real axis, but in contrast to the classical orthogonal polynomials of the Askey scheme, the -1 dual Hahn polynomials do not exhibit the Leonard duality property ...
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov   +2 more
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On Jacobi and continuous Hahn polynomials [PDF]

Proceedings of the American Mathematical Society, 1996
The inter-relation between the Jacobi polynomials and the continuous Hahn polynomials via the Fourier transform is exploited to deduce the orthogonality relation of the latter from that of the former and the use of Parseval's relation. This is an additional independent case of the proof of this important relation whereby the general theory of special ...
H.T. Koelink
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A shifted fractional-order Hahn functions Tau method for time-fractional PDE with nonsmooth solution [PDF]

Iranian Journal of Numerical Analysis and Optimization, 2023
In this paper, a new orthogonal system of nonpolynomial basis functions is introduced and used to solve a class of time-fractional partial differential equations that have nonsmooth solutions.
N. Mollahasani
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