A new bound for the Laguerre polynomials

Michalska, Małgorzata; Szynal, Jan

doi:10.1016/s0377-0427(00)00670-1

Cited by 16 publications

(9 citation statements)

References 6 publications

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“…The generalized Laguerre polynomials constitute a complete orthogonal set of functions on the semiinfinite interval [0, 1) [20,21]. The convolution structures of the Laguerre polynomials were presented in Ref.…”

Section: The Definition and Properties Of The Generalizedmentioning

confidence: 99%

The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations

Khader

2013

Journal of Computational and Nonlinear Dynamics

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In this paper, an efficient numerical method for solving the fractional delay differential equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based on the derived approximate formula of the Laguerre polynomials. The properties of Laguerre polynomials are utilized to reduce FDDEs to a linear or nonlinear system of algebraic equations. Special attention is given to study the error and the convergence analysis of the proposed method. Several numerical examples are provided to confirm that the proposed method is in excellent agreement with the exact solution.

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Section: The Definition and Properties Of The Generalizedmentioning

confidence: 99%

The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations

Khader

2013

Journal of Computational and Nonlinear Dynamics

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“…[1]). Michalska and Szynal [14] gave a better inequality for 0. Unfortunately, their bounds are not explicit and ought to be estimated by themselves.…”

Section: Introductionmentioning

confidence: 98%

Inequalities for orthonormal Laguerre polynomials

Krasikov

2007

Journal of Approximation Theory

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“…thanks to (17) and using (19). Next, by means of (23) combined with (20) with k = 1 and j = 0, we get…”

Section: Variants Of Rodrigues' Formula and Recurrence Formulasmentioning

confidence: 97%

On some analytic properties of slice poly‐regular Hermite polynomials

Hamyani

Ghanmi

2018

Math Methods in App Sciences

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We consider a quaternionic analogue of the univariate complex Hermite polynomials and study some of their analytic properties in some detail. We obtain their integral representation as well as the operational formulas of exponential and Burchnall types they obey. We show that they form an orthogonal basis of the slice Hilbert space L2false(LI;e−false|q|2dλIfalse) of all quaternionic‐valued functions defined the whole quaternions space and subject to norm boundedness with respect to the Gaussian measure on a given slice as well as of the full left quaternionic Hilbert space L2false(double-struckH;e−false|q|2dλfalse) of square integrable functions on quaternions with respect to the Gaussian measure on the whole double-struckH≡R4. We also provide different types of generating functions. Remarkable identities, including quadratic recurrence formulas of Nielsen type, are also derived.

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A new bound for the Laguerre polynomials

Cited by 16 publications

References 6 publications

The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations

The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations

Inequalities for orthonormal Laguerre polynomials

On some analytic properties of slice poly‐regular Hermite polynomials

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