Classical Special Functions and Lie Groups
نویسندگان
چکیده
The classical orthogonal functions of mathematical physics are closely related to Lie groups. Specifically, they are matrix elements of, or basis vectors for, unitary irreducible representations of lowdimensional Lie groups. We illustrate this connection for: The Wigner functions, spherical harmonics, and Legendre polynomials; the Bessel functions; and the Hermite polynomials. These functions are associated with the Lie groups: the rotation group SO(3) in three-space and its covering group SU(2); the Euclidean group in the plane E(2) or ISO(2); and the Heisenberg group H4.
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