Integrals of Products of Bessel Functions

Jackson, A.D.; Maximon, L. C.

doi:10.1137/0503043

Cited by 44 publications

(26 citation statements)

References 7 publications

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“…On the other hand, there are many other applications in nuclear physics that encounter these types of integrals amongst which are distorted wave calculations [2] and nuclear response function calculations [3]. These types of integrals have in the past been calculated analytically (many references exist, see for example references [2] and [4][5][6][7][8][9][10][11]), or numerically using complex-plane methods (see for example references [12][13][14]). In this paper, an additional advantage to the plane wave expansion is presented, whereby the expansion itself is used to derive analytical solutions to integrals over spherical Bessel functions and identities involving them.…”

Section: Introductionmentioning

confidence: 99%

The plane wave expansion, infinite integrals and identities involving spherical Bessel functions

Mehrem

2011

Applied Mathematics and Computation

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This paper shows that the plane wave expansion can be a useful tool in obtaining analytical solutions to infinite integrals over spherical Bessel functions and the derivation of identites for these functions. The integrals are often used in nuclear scattering calculations, where an analytical result can provide an insight into the reaction mechanism. A technique is developed whereby an integral over several special functions which cannot be found in any standard integral table can be broken down into integrals that have existing analytical solutions.

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Section: Introductionmentioning

confidence: 99%

The plane wave expansion, infinite integrals and identities involving spherical Bessel functions

Mehrem

2011

Applied Mathematics and Computation

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“…The shift operator can be evaluated in closed form using results derived in Jackson and Maximon (1972). In their work, closed-form results are found for the triple-product integral given by ∞ 0 J n 1 (k 1 ρ)J n 2 (k 2 ρ)J n 3 (k 3 ρ)ρdρ.…”

Section: The Shift Operatormentioning

confidence: 99%

“…Closed-form results are given in Jackson and Maximon (1972), to which the interested reader is referred. (74) guarantees that the indices add up to zero.…”

Section: The Shift Operatormentioning

confidence: 99%

Two-Dimensional Fourier Transforms in Polar Coordinates

Baddour¹

2011

Advances in Imaging and Electron Physics

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“…Since different authors found different, relevant expressions for integrals involving three Bessel functions [21][22][23], we repeat here the derivation for integrals involving four spherical Bessel functions from the former ones.…”

Section: Expansion Of the Scattering Kernelmentioning

confidence: 99%

Solving the homogeneous Boltzmann equation with arbitrary scattering kernel

Hohenegger

2009

Phys. Rev. D

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With applications in astroparticle physics in mind, we generalize a method for the solution of the nonlinear, space homogeneous Boltzmann equation with isotropic distribution function to arbitrary matrix elements. The method is based on the expansion of the matrix element in terms of two cosines of the "scattering angles". The scattering functions used by previous authors in particle physics for matrix elements in Fermi-approximation are retrieved as lowest order results in this expansion. The method is designed for the unified treatment of reactive mixtures of particles obeying different scattering laws, including the quantum statistical terms for blocking or stimulated emission, in possibly large networks of Boltzmann equations. Although our notation is the relativistic one, as it is used in astroparticle physics, the results can also be applied in the classical case

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Integrals of Products of Bessel Functions

Cited by 44 publications

References 7 publications

The plane wave expansion, infinite integrals and identities involving spherical Bessel functions

The plane wave expansion, infinite integrals and identities involving spherical Bessel functions

Two-Dimensional Fourier Transforms in Polar Coordinates

Solving the homogeneous Boltzmann equation with arbitrary scattering kernel

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