caa a22 4500 477076726 CHVBK 20180405111440.0 cr unu---uuuuu 170330e19960601xx s 000 0 eng 10.1007/BF00047669 doi (NATIONALLICENCE)springer-10.1007/BF00047669 Feinsilver Philip Department of Mathematics, Southern Illinois University, 62901, Carbondale, IL, U.S.A. aut Lie algebras and recurrence relations IV: Representations of the Euclidean group and Bessel functions [Elektronische Daten] [Philip Feinsilver] Representations of a complex form of the Lie algebra of the Euclidean group of the plane are found. Bases for the corresponding Hilbert spaces are given in terms of Lommel polynomials and Bessel functions. An element of the Lie algebra is interpreted as a quantum random variable leading to the Lommel distributions. The tails of these distributions and limit theorems are studied. Applications to electronic music are noted, as well as connection with quantum mechanics on a one-dimensional lattice. Kluwer Academic Publishers, 1996 Euclidean group nationallicence Bessel functions nationallicence Lommel polynomials nationallicence quantum probability nationallicence Airy function nationallicence limit theorems nationallicence large deviations nationallicence electronic music nationallicence Acta Applicandae Mathematica Kluwer Academic Publishers; gopher://gopher.wkap.nl 43/3(1996-06-01), 289-316 0167-8019 43:3<289 1996 43 10440 https://doi.org/10.1007/BF00047669 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00047669 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Feinsilver Philip Department of Mathematics, Southern Illinois University, 62901, Carbondale, IL, U.S.A aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers; gopher://gopher.wkap.nl 43/3(1996-06-01), 289-316 0167-8019 43:3<289 1996 43 10440 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer