Bessel Functions

Nikiforov, A. F.; Uvarov, V.B.

doi:10.1007/978-1-4757-1595-8_3

Cited by 14 publications

(20 citation statements)

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“…The classical discrete orthogonal polynomials of one variable can be de¯ned as the polynomial solutions of the following di®erence equation 11,12 ðxÞÁrp n ðxÞ þ ðxÞÁp n ðxÞ þ n p n ðxÞ ¼ 0 ð1Þ…”

Section: The Classical Discrete Orthogonal Polynomials Of One Variablementioning

confidence: 99%

“…(2) depending on the normalizing factors B n . For the backward di®erence operator O we have the property 11,12 r n fðxÞ ¼ X n k¼0 n k ðÀ1Þ k fðx À kÞ ð 3Þ…”

Section: The Classical Discrete Orthogonal Polynomials Of One Variablementioning

confidence: 99%

“…The polynomials p n ðxÞ satisfy an orthogonality relation of the form For univariate Charlier and Meixner polynomials, Nikiforov et al 11 introduced some basis information listed in Table 1. Their weight functions are de¯ned in the following discrete domain…”

Section: The Classical Discrete Orthogonal Polynomials Of One Variablementioning

confidence: 99%

“…14 and 15. Although bivariate orthogonal polynomials play an important role in applications such as numerical analysis, optics, and quantum mechanics, 11,12,18 much less attention has been paid to the application of bivariate orthogonal polynomials in image analysis.…”

Section: Introductionmentioning

confidence: 99%

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Image Description With Nonseparable Two-Dimensional Charlier and Meixner Moments

Zhu

Liu

et al. 2011

Int. J. Patt. Recogn. Artif. Intell.

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This paper presents two new sets of nonseparable discrete orthogonal Charlier and Meixner moments describing the images with noise and that are noise-free. The basis functions used by the proposed nonseparable moments are bivariate Charlier or Meixner polynomials introduced by Tratnik et al. This study discusses the computational aspects of discrete orthogonal Charlier and Meixner polynomials, including the recurrence relations with respect to variable x and order n. The purpose is to avoid large variation in the dynamic range of polynomial values for higher order moments. The implementation of nonseparable Charlier and Meixner moments does not involve any numerical approximation, since the basis function of the proposed moments is orthogonal in the image coordinate space. The performances of Charlier and Meixner moments in describing images were investigated in terms of the image reconstruction error, and the results of the experiments on the noise sensitivity are given.Keywords : Bivariate discrete orthogonal polynomials; nonseparable discrete orthogonal moments; Charlier; Meixner; three-term recurrence relations; second order linear partial di®erence equations.

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Section: The Classical Discrete Orthogonal Polynomials Of One Variablementioning

confidence: 99%

“…(2) depending on the normalizing factors B n . For the backward di®erence operator O we have the property 11,12 r n fðxÞ ¼ X n k¼0 n k ðÀ1Þ k fðx À kÞ ð 3Þ…”

Section: The Classical Discrete Orthogonal Polynomials Of One Variablementioning

confidence: 99%

Section: The Classical Discrete Orthogonal Polynomials Of One Variablementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Image Description With Nonseparable Two-Dimensional Charlier and Meixner Moments

Zhu

Liu

et al. 2011

Int. J. Patt. Recogn. Artif. Intell.

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“…This powerful mathematical tool enables us to solve second-order differential equations. Let us consider the differential equation [46] {︁ 𝑑…”

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confidence: 99%

Approximate Analytical Solutions to the Generalized Pöschl—Teller Potential in D Dimensions

Hassanabadi¹,

Hoda²,

Li-zhu³

2012

Chinese Phys. Lett.

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Triaxial nuclei and analytical solutions of the conformable fractional Bohr Hamiltonian with some exponential-type potentials

2023

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Bessel Functions

Cited by 14 publications

References 0 publications

Image Description With Nonseparable Two-Dimensional Charlier and Meixner Moments

Image Description With Nonseparable Two-Dimensional Charlier and Meixner Moments

Approximate Analytical Solutions to the Generalized Pöschl—Teller Potential in D Dimensions

Triaxial nuclei and analytical solutions of the conformable fractional Bohr Hamiltonian with some exponential-type potentials

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