scholarly journals Fast associated classical orthogonal polynomial transforms

2021 ◽  
pp. 113831
Author(s):  
Brock Klippenstein ◽  
Richard Mikaël Slevinsky
Keyword(s):  
Orthogonal Polynomial ◽  
Classical Orthogonal Polynomial

scholarly journals A characterization of the four Chebyshev orthogonal families

2005 ◽  
Vol 2005 (13) ◽  
pp. 2071-2079 ◽  
Author(s):  
E. Berriochoa ◽  
A. Cachafeiro ◽  
J. M. Garcia-Amor
Keyword(s):  
Orthogonal Polynomial ◽  
Orthogonal Polynomials ◽  
Linear Combinations ◽  
Classical Orthogonal Polynomial ◽  
Polynomial Sequences ◽  
Fixed Length ◽  
Constant Coefficients ◽  
Fourth Kind

We obtain a property which characterizes the Chebyshev orthogonal polynomials of first, second, third, and fourth kind. Indeed, we prove that the four Chebyshev sequences are the unique classical orthogonal polynomial families such that their linear combinations, with fixed length and constant coefficients, can be orthogonal polynomial sequences.

scholarly journals L-classical d-orthogonal polynomial sets of Sheffer type

Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 881-895
Author(s):  
Youssèf Cheikh ◽  
Inès Gam
Keyword(s):  
Differential Equation ◽  
Orthogonal Polynomial ◽  
Order Differential Equation ◽  
Derivative Operator ◽  
Classical Orthogonal Polynomial ◽  
First Case ◽  
Lowering Operators ◽  
Lowering Operator

In this paper, we characterize L-classical d-orthogonal polynomial sets of Sheffer type where L being a lowering operator commutating with the derivative operator D and belonging to {D,eD-1, sin(D)}. For the first case we state a (d+1)-order differential equation satisfied by the corresponding polynomials. We, also, show that, with these three lowering operators, all the orthogonal polynomial sets are classified as L-classical orthogonal polynomial sets.

scholarly journals HAHN'S PROBLEM WITH RESPECT TO SOME PERTURBATIONS OF THE RAISING OPERATOR \(X-c\)

2020 ◽  
Vol 6 (2) ◽  
pp. 15
Author(s):  
Baghdadi Aloui ◽  
Jihad Souissi
Keyword(s):  
Orthogonal Polynomial ◽  
Complex Number ◽  
Classical Orthogonal Polynomial ◽  
Arbitrary Complex Number ◽  
Raising Operators ◽  
Charlier Polynomial ◽  
Arbitrary Complex ◽  
Raising Operator

In this paper, we study the Hahn's problem with respect to some raising operators perturbed of the operator \(X-c\), where \(c\) is an arbitrary complex number. More precisely, the two following characterizations hold: up to a normalization, the \(q\)-Hermite (resp. Charlier) polynomial is the only \(H_{\alpha,q}\)-classical (resp. \(\mathcal{S}_{\lambda}\)-classical) orthogonal polynomial, where \(H_{\alpha, q}:=X+\alpha H_q\) and \(\mathcal{S}_{\lambda}:=(X+1)-\lambda\tau_{-1}.\)

Pengaruh Pemberian Kunyit (Curcuma domestica) terhadap Beberapa Kualitas Fisik dan Organoleptik Bakso Daging Itik

2013 ◽  
Vol 8 (1) ◽  
pp. 16-24
Author(s):  
Sari Murti ◽  
Suharyanto Suharyanto ◽  
Desia Kaharuddin
Keyword(s):  
Orthogonal Polynomial

ABSTRAKPenelitian ini bertujuan untuk mengevaluasi level kunyit yang tepat sehingga dapat meningkatkan kualitas bakso daging itik. Percobaan ini menggunakan Rancangan Acak Lengkap, yang terdiri dari empat perlakuan yaitu P0 (tanpa pemberian kunyit), P1 (pemberian kunyit taraf 2,5%), P2 (pemberian kunyit taraf 5%), dan P3 (pemberian kunyittaraf 7,5%), masing-masing perlakuan terdiri dari tiga ulangan. Hasil penelitian menunjukkan bahwa pemberian kunyit berpengaruh tidak nyata (P>0,05) terhadap variabel susut masak, daya mengikat air, pH dan tekstur bakso daging itik, tetapi nyata (P<0,05) meningkatkan skor warna, menurunkan derajat keamisan dan variabel sifat organoleptik rasa. Hasil yang berpengaruh nyata diuji lanjut menggunakan Orthogonal polynomial dengan menghasilkan persamaan linear dan kuadratik. Dari hasil penelitian disimpulkan bahwa penambahan kunyit 2,5% hingga 7,5% tidak menurunkan kualitas fisik (susut masak, pH, dan DMA). Penambahan kunyit 2,5% dapat mempertahankan cita rasa dan penerimaan umum panelis terhadap bakso daging itik.Kata kunci : Kunyit (Curcuma domestica), kualitas fisik, daging itik

A Useful Curve Fitting Method for Concrete Uniaxial Compressive Experiment Data

2011 ◽  
Vol 291-294 ◽  
pp. 1015-1020 ◽  
Author(s):  
Chong Jin ◽  
Hong Wang ◽  
Xiao Zhou Xia
Keyword(s):  
Experimental Data ◽  
Orthogonal Polynomial ◽  
Least Square ◽  
Base Function ◽  
Concrete Material ◽  
Fitting Method ◽  
Orthogonal Base ◽  
The Matrix ◽  
Uniform Function ◽  
Curve Fitting Method

Based on the superiority avoiding the matrix equation to be morbid for those fitting functions constructed by orthogonal base, the Legendre orthogonal polynomial is adopted to fit the experimental data of concrete uniaxial compression stress-strain curves under the frame of least-square. With the help of FORTRAN programming, 3 series of experimental data is fitted. And the fitting effect is very satisfactory when the item number of orthogonal base is not less than 5. What’s more, compared with those piecewise fitting functions, the Legendre orthogonal polynomial fitting function obtained can be introduced into the nonlinear harden-soften character of concrete constitute law more convenient because of its uniform function form and continuous derived feature. And the fitting idea by orthogonal base function will provide a widely road for studying the constitute law of concrete material.

scholarly journals $q$ -Racah Ensemble and Discrete Painlevé Equation

2019 ◽  
Vol 2020 (24) ◽  
pp. 9797-9843 ◽  
Author(s):  
Anton Dzhamay ◽  
Alisa Knizel
Keyword(s):  
Orthogonal Polynomial ◽  
Lax Pair ◽  
Painlevé Equations ◽  
Painlevé Equation ◽  
Painleve Equations ◽  
Symmetry Structure ◽  
The One ◽  
The Relationship ◽  
Gap Probabilities ◽  
Discrete Painlevé Equation

Abstract The goal of this paper is to investigate the missing part of the story about the relationship between the orthogonal polynomial ensembles and Painlevé equations. Namely, we consider the $q$-Racah polynomial ensemble and show that the one-interval gap probabilities in this case can be expressed through a solution of the discrete $q$-P$\left (E_7^{(1)}/A_{1}^{(1)}\right )$ equation. Our approach also gives a new Lax pair for this equation. This Lax pair has an interesting additional involutive symmetry structure.

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