Results 21 to 30 of about 906 (173)

On the Complex Zeros of Some Families of Orthogonal Polynomials

Abstract and Applied Analysis, 2010
The complex zeros of the orthogonal Laguerre polynomials 𝐿𝑛(𝑎)(𝑥) for ...
Eugenia N. Petropoulou
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Derivatives of Orthonormal Polynomials and Coefficients of Hermite-Fejér Interpolation Polynomials with Exponential-Type Weights

Journal of Inequalities and Applications, 2010
Let , and let be an even function. In this paper, we consider the exponential-type weights , and the orthonormal polynomials of degree with respect to .
Sakai R, Jung HS
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Orthonormal polynomials with generalized Freud-type weights

Journal of Approximation Theory, 2003
The authors study polynomials, orthonormal with respect to a generalized Freud-type weight \(W_{rQ}^2(x)=| x| ^{2r}\exp(-2Q(x)),\) where \(r>-1/2\) and \(\exp(-2Q(x))\) is a Freud weight. They prove infinite-finite range inequalities, estimates of Christoffel functions, the largest zeros and spacing of zeros for those orthonormal polynomials.
Kasuga, T., Sakai, R.
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Orthonormal Polynomial Expansions and Lognormal Sum Densities [PDF]

, 2019
Approximations for an unknown density $g$ in terms of a reference density $f_ $ and its associated orthonormal polynomials are discussed. The main application is the approximation of the density $f$ of a sum $S$ of lognormals which may have different variances or be dependent.
Asmussen, Søren, Goffard, Pierre-Olivier, Laub, Patrick   +2 more
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Orthonormal polynomial basis in local Dirichlet spaces

Acta Scientiarum Mathematicarum, 2021
We provide an orthogonal basis of polynomials for the local Dirichlet space $\mathcal D_\zeta$. These polynomials have numerous interesting features and a very unique algebraic pattern. We obtain the recurrence relation, the generating function, a simple formula for their norm, and explicit formulae for the distance and the orthogonal projection onto ...
Fricain, Emmanuel, Mashreghi, Javad
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A numerical scheme to simulate the distributed-order time 2D Benjamin Bona Mahony Burgers equation with fractional-order space

Mathematical Modelling and Analysis
In this study, a new class of the Benjamin Bona Mahony Burgers equation is introduced, which considers the distributedorder in the time variable and fractional-order space in the Caputo form in the 2D case. The 2D-modified orthonormal normalized shifted
Hais Azin, Omid Baghani, Ali Habibirad
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Smooth Wavelet Approximations of Truncated Legendre Polynomials via the Jacobi Theta Function

Abstract and Applied Analysis, 2014
The family of nth order q-Legendre polynomials are introduced. They are shown to be obtainable from the Jacobi theta function and to satisfy recursion relations and multiplicatively advanced differential equations (MADEs) that are analogues of the ...
David W. Pravica, Njinasoa Randriampiry, Michael J. Spurr   +2 more
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On the Uniform Convergence of the Fourier Series by the System of Polynomials Generated by the System of Laguerre Polynomials [PDF]

Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2020
Let w(x) be the Laguerre weight function, 1 /le p < ∞, and Lpw be the space of functions f, p-th power of which is integrable with the weight function w(x) on the non-negative axis.
Gadzhimirzaev, Ramis Makhmudovich
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Logarithmic Bernstein functions for fractional Rosenau–Hyman equation with the Caputo–Hadamard derivative

Results in Physics
In this study, the Caputo–Hadamard derivative is fittingly used to define a fractional form of the Rosenau–Hyman equation. To solve this equation, the orthonormal logarithmic Bernstein functions (BFs) are created as a suitable basis for handling this ...
M.H. Heydari, F. Heydari, O. Bavi, M. Bayram   +3 more
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Orthonormal Ultraspherical Operational Matrix Algorithm for Fractal–Fractional Riccati Equation with Generalized Caputo Derivative

Fractal and Fractional, 2021
Herein, we developed and analyzed a new fractal–fractional (FF) operational matrix for orthonormal normalized ultraspherical polynomials. We used this matrix to handle the FF Riccati differential equation with the new generalized Caputo FF derivative ...
Youssri Hassan Youssri
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