Analytical properties of the two-variables Jacobi matrix polynomials with applications
Demonstratio Mathematica, 2021 In the current study, we introduce the two-variable analogue of Jacobi matrix polynomials. Some properties of these polynomials such as generating matrix functions, a Rodrigue-type formula and recurrence relations are also derived.
Abdalla Mohamed, Hidan Muajebah
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An algebraic treatment of the Askey biorthogonal polynomials on the unit circle
Forum of Mathematics, Sigma, 2021 A joint algebraic interpretation of the biorthogonal Askey polynomials on the unit circle and of the orthogonal Jacobi polynomials is offered. It ties their bispectral properties to an algebra called the meta-Jacobi algebra $m\mathfrak {J}$ .
Luc Vinet, Alexei Zhedanov
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A note on the convergence of Phillips operators by the sequence of functions via q-calculus
Demonstratio Mathematica, 2022 The basic aim of this study is to include nonnegative real parameters to allow for approximation findings of the Stancu variant of Phillips operators.
Kiliçman Adem +2 more
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On the kernel of the $(\kappa ,a)$ -Generalized fourier transform
Forum of Mathematics, Sigma, 2023 For the kernel $B_{\kappa ,a}(x,y)$ of the $(\kappa ,a)$ -generalized Fourier transform $\mathcal {F}_{\kappa ,a}$ , acting in $L^{2}(\mathbb {R}^{d})$ with the weight $|x|^{a-2}v_{\kappa }(x)$ , where $v_{\kappa }$
Dmitry Gorbachev +2 more
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A note on Eulerian numbers and Toeplitz matrices
Special Matrices, 2020 This note presents a new formula of Eulerian numbers derived from Toeplitz matrices via Riordan array approach.
He Tian-Xiao, Shiue Peter J.-S.
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An efficient algorithm for solving the conformable time-space fractional telegraph equations
Moroccan Journal of Pure and Applied Analysis, 2021 In this paper, an efficient algorithm is proposed for solving one dimensional time-space-fractional telegraph equations. The fractional derivatives are described in the conformable sense.
Saad Abdelkebir, Brahim Nouiri
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Orthogonal polynomials for exponential weights x2α(1 – x2)2ρe–2Q(x) on [0, 1)
Open Mathematics, 2020 Let Wα,ρ = xα(1 – x2)ρe–Q(x), where α > –12$\begin{array}{} \displaystyle \frac12 \end{array}$ and Q is continuous and increasing on [0, 1), with limit ∞ at 1.
Liu Rong
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A System of Multivariable Krawtchouk Polynomials and a Probabilistic Application [PDF]
, 2011 The one variable Krawtchouk polynomials, a special case of the $_2F_1$ function did appear in the spectral representation of the transition kernel for a Markov chain studied a long time ago by M. Hoare and M. Rahman.
Grünbaum, F. Alberto, Rahman, Mizan
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Orthogonality Relations for Multivariate Krawtchouk Polynomials [PDF]
, 2011 The orthogonality relations of multivariate Krawtchouk polynomials are discussed. In case of two variables, the necessary and sufficient conditions of orthogonality is given by Gr\"unbaum and Rahman in [SIGMA 6 (2010), 090, 12 pages, arXiv:1007.4327]. In
Mizukawa, Hiroshi
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q-Functions and Distributions, Operational and Umbral Methods
Mathematics, 2021 The use of non-standard calculus means have been proven to be extremely powerful for studying old and new properties of special functions and polynomials.
Giuseppe Dattoli +3 more
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