Results 31 to 40 of about 40,909 (200)

Onsager's algebra and partially orthogonal polynomials [PDF]

, 2002
The energy eigenvalues of the superintegrable chiral Potts model are determined by the zeros of special polynomials which define finite representations of Onsager's algebra. The polynomials determining the low-sector eigenvalues have been given by Baxter
Albertini G., Dolan L., G. VON GEHLEN
core   +2 more sources

Dispersion Estimates for the Discrete Laguerre Operator [PDF]

, 2016
We derive an explicit expression for the kernel of the evolution group $\exp(-\mathrm{i} t H_0)$ of the discrete Laguerre operator $H_0$ (i.e. the Jacobi operator associated with the Laguerre polynomials) in terms of Jacobi polynomials.
Kostenko, Aleksey, Teschl, Gerald
core   +2 more sources

A conjecture on Exceptional Orthogonal Polynomials [PDF]

, 2012
Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of Sturm-Liouville problems and generalize in this sense the classical families of Hermite, Laguerre and Jacobi. They also generalize the family of CPRS orthogonal polynomials.
A. González-López, A. Ronveaux, A. Ronveaux, A. Turbiner, B. Midya, C. Quesne, C. Quesne, C. Quesne, C.-L. Ho, C.-L. Ho, D. Dutta, D. Dutta, D. Gómez-Ullate, D. Gómez-Ullate, D. Gómez-Ullate, D. Gómez-Ullate, D. Gómez-Ullate, D. Gómez-Ullate, D. Gómez-Ullate, D. Gómez-Ullate, D. Gómez-Ullate, David Gómez-Ullate, F.A. Grünbaum, G. Szegő, J.F. Cariñena, J.M. Fellows, L.E. Gendenshtein, M.G. Krein, M.M. Crum, N. Kamran, Niky Kamran, P. Lesky, R. Sasaki, Robert Milson, S. Bochner, S. Odake, S. Odake, S. Odake, S.Y. Dubov, V.B. Uvarov, V.E. Adler, W.N. Everitt, Y. Grandati   +42 more
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Chained-Function Filter Synthesis Based on the Modified Jacobi Polynomials [PDF]

Radioengineering, 2018
A new class of filter functions with pass-band ripple which derives its origin from a method of determining the chained function lowpass filters described by Guglielmi and Connor is introduced.
G. Perenic, N. Stamenkovic, N. Stojanovic, N. Denic   +3 more
doaj  

Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space

International Journal of Mathematics and Mathematical Sciences, 2004
A new method for constructing Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space is presented. In earlier research, we only dealt with scalar-valued weight functions.
Fred Brackx, Nele De Schepper, Frank Sommen   +2 more
doaj   +1 more source

The Jacobi inversion formula

, 1999
We look for spectral type differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the classical Jacobi weight function together with point masses ...
Koekoek, J., Koekoek, R.
core   +2 more sources

Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : III [PDF]

, 2016
In a previous paper, we presented conjectures of the recurrence relations with constant coefficients for the multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types.
Odake, Satoru
core   +3 more sources

On the Integral Representation of Jacobi Polynomials

Mathematics
In this paper, we present a new integral representation for the Jacobi polynomials that follows from Koornwinder’s representation by introducing a suitable new form of Euler’s formula.
Enrico De Micheli
doaj   +1 more source

Extended Jacobi Functions via Riemann-Liouville Fractional Derivative

Abstract and Applied Analysis, 2013
By means of the Riemann-Liouville fractional calculus, extended Jacobi functions are de…fined and some of their properties are obtained. Then, we compare some properties of the extended Jacobi functions extended Jacobi polynomials.
Bayram Çekim, Esra Erkuş-Duman
doaj   +1 more source

An elementary representation of the higher-order Jacobi-type differential equation

, 2017
We investigate the differential equation for the Jacobi-type polynomials which are orthogonal on the interval $[-1,1]$ with respect to the classical Jacobi measure and an additional point mass at one endpoint.
Markett, Clemens
core   +1 more source