Some integrals involving Coulomb functions associated with the three-dimensional proper Lorentz group

DOI10.3934/math.2020362zbMath1484.33010OpenAlexW3040073456MaRDI QIDQ2132137

Jae Won Lee, Junesang Choi, I. A. Shilin

Publication date: 27 April 2022

Published in: AIMS Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/math.2020362

zbMATH Keywords

Whittaker functionCoulomb functionsmatrix elements of representationBessel-Clifford functionsAppell function \(F_1\)bases transformationsBessel-Macdonald integral transformfirst and the second Bessel-Clifford integral transformsproper Lorenz group

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Integral transforms of special functions (44A20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (4)

On changing between bases of the space of representations of group \(\mathrm{SO}(2,2)\) ⋮ Maximal subalgebras in \(\mathfrak{s}\mathfrak{o}(2,1)\), addition theorems and Bessel-Clifford functions ⋮ Evaluation of integral transforms using special functions with applications to biological tissues ⋮ Method of continual addition theorems and integral relations between the Coulomb functions and the Appell function \(F_1\)

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the evaluation of integrals with Coulomb Sturmian radial functions
• Coulomb and Bessel functions of complex arguments and order
• A pair of generalized Hankel-Clifford transformations and their applications
• Remarks on some associated Laguerre integral results
• Representation of the Coulomb matrix elements by means of Appell hypergeometric function \(F_2\)
• Some connections between the spherical and parabolic bases on the cone expressed in terms of the Macdonald function
• THE THERMODYNAMICS OF THERMAL INSTABILITY IN LIQUIDS
• Symmetry scattering on the hyperboloid SO(2,1)/SO(2) in different coordinate systems
• Coulomb wave functions with complex values of the variable and the parameters
• Connection formulas between Coulomb wave functions
• Certain relations between Bessel and Whittaker functions related to some diagonal and block-diagonal 3\times3-matrices
• Certain connections between the spherical and hyperbolic bases on the cone and formulas for related special functions
• INTEGRAL RELATIONS FOR THE WHITTAKER FUNCTIONS AND THE REPRESENTATIONS OF THE THREE-DIMENSIONAL LORENTZ GROUP

This page was built for publication: Some integrals involving Coulomb functions associated with the three-dimensional proper Lorentz group