A new class of orthogonal polynomials: The Bessel polynomials

Krall, H. L.; Frink, Orrin

doi:10.1090/s0002-9947-1949-0028473-1

Cited by 322 publications

(158 citation statements)

References 8 publications

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“…For further use, we need to introduce some Bessel functions [1,23,31,32,5]. Those special functions are going to play a major role throughough this article.…”

Section: Bessel Polynomialsmentioning

confidence: 99%

Some properties of angular integrals

Bergère¹,

Eynard²

2009

J. Phys. A: Math. Theor.

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Abstract:We find new representations for Itzykson-Zuber like angular integrals for arbitrary β, in particular for the orthogonal group O(n), the unitary group U(n) and the symplectic group Sp(2n). We rewrite the Haar measure integral, as a flat Lebesge measure integral, and we deduce some recursion formula on n. The same methods gives also the Shatashvili's type moments. Finally we prove that, in agreement with Brezin and Hikami's observation, the angular integrals are linear combinations of exponentials whose coefficients are polynomials in the reduced variables (x i − x j )(y i − y j ).

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“…For further use, we need to introduce some Bessel functions [1,23,31,32,5]. Those special functions are going to play a major role throughough this article.…”

Section: Bessel Polynomialsmentioning

confidence: 99%

Some properties of angular integrals

Bergère¹,

Eynard²

2009

J. Phys. A: Math. Theor.

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“…From Equation (12), it can be easily seen that y n,k (z) coincides, for k = 0, with the canonical Bessel polynomial (BP ) of order n [9,10]:…”

Section: Definitionmentioning

confidence: 99%

“…Actually, there is a strong interrelationship between these sequences of special polynomials, the analytical properties of the former paralleling and generalizing those of the latter. Finally, combining Equations (6), (9), and (11) yields the following closed-form analytical expression of the IMSBF of order n:…”

Section: Definitionmentioning

confidence: 99%

“…In order to derive the differential equation defining y n,k (·), let us first introduce the conventional Bessel operator [9,10]:…”

Section: Analytical Propertiesmentioning

confidence: 99%

“…It is not difficult to find out that formulas (19)-(23) degenerate into the well-known recurrence equations for canonical BPs as the index k is set to zero [9]. Starting from the expansion (12), the incomplete reverse Bessel polynomials (IRBPs) can be defined as the class of functions (see Fig.…”

Section: Analytical Propertiesmentioning

confidence: 99%

See 2 more Smart Citations

Incomplete Bessel Polynomials: A New Class of Special Polynomials for Electromagnetics

Caratelli¹,

Babur²,

Shibelgut³

et al. 2015

PIER M

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Abstract-A new class of incomplete Bessel polynomials is introduced, and its application to the solution of electromagnetic problems regarding transient wave radiation phenomena in truncated spherical structures is discussed. The general definition and main analytical properties of said special functions are provided. The definition is such that the interrelationships between the incomplete polynomials parallel, as far as it is feasible, those for canonical Bessel polynomials.

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Some Properties and Generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers

Guo

2018

Mathematical Analysis and Applications

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A new class of orthogonal polynomials: The Bessel polynomials

Cited by 322 publications

References 8 publications

Some properties of angular integrals

Some properties of angular integrals

Incomplete Bessel Polynomials: A New Class of Special Polynomials for Electromagnetics

Some Properties and Generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers

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