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Isotopic generalization of the Legendre, Jacobi, and Bessel functions. (English) Zbl 0843.33006

The authors describe in detail the group of rotations of three-dimensional isoEuclidean space and the group locally isomorphic to it, consisting of isounitary isomodular \(2\times 2\) matrices. They also study the group of quasiunitary matrices and the group of isometric transformations of isoEuclidean plane. These groups are used (following the case of the groups \(SO(3)\), \(SU(2)\) and \(M(2)\)) to define and to study the Lie-isotopic generalization of the Legendre, Jacobi and Bessel functions. Basic properties and functional relations for these functions are given. They are similar to these for their usual counterparts. The authors state that their generalizations of the Legendre Jacobi and Bessel functions can be used in formulations of the nonpotential scattering theory when one considers non-zero isoangular momenta.
Reviewer: A.Klimyk (Kiev)

MSC:

33C80 Connections of hypergeometric functions with groups and algebras, and related topics
81U99 Quantum scattering theory
81V35 Nuclear physics
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