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On Lie algebras and some special functions of mathematical physics

Author: Willard Miller
Publisher: Providence, R.I. : American Mathematical Society, 1964.
Series: Memoirs of the American Mathematical Society, no. 50.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
The factorization method for second order ordinary differential equations is shown to be related to the representation theory of four Lie algebras: the Lie algebras of the Euclidean groups in 2 and 3-space, the Lie algebra of the rotation group in 3-space, and a certain 4-dimensional solvable Lie algebra. Recursion relations and generating functions for the hypergeometric, confluent hypergeometric, Bessel, and  Read more...
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Additional Physical Format: Online version:
Miller, Willard.
On Lie algebras and some special functions of mathematical physics.
Providence, R.I. : American Mathematical Society, 1964
(OCoLC)652482730
Document Type: Book
All Authors / Contributors: Willard Miller
OCLC Number: 1312557
Description: 43 pages ; 26 cm.
Contents: Introduction --
A relation between Lie algebras and special functions --
The representation theory of [italic capital]O₃ --
Type [italic capital]A and [italic capital]B factorizations --
The representation theory of [italic capital]H₄ --
Type [italic capital]C′ and [italic capital]D′ factorizations --
The representation theory of [italic capital]T₃ --
Type [italic capital]C′′ factorizations --
Generating functions for type [italic capital]A-[italic capital]D eigenfunctions --
The representation theory of [italic capital]T₆ --
Type [italic capital]E and [italic capital]F factorizations --
Appendix.
Series Title: Memoirs of the American Mathematical Society, no. 50.
Responsibility: by Willard Miller.

Abstract:

The factorization method for second order ordinary differential equations is shown to be related to the representation theory of four Lie algebras: the Lie algebras of the Euclidean groups in 2 and 3-space, the Lie algebra of the rotation group in 3-space, and a certain 4-dimensional solvable Lie algebra. Recursion relations and generating functions for the hypergeometric, confluent hypergeometric, Bessel, and parabolic cylinder functions are obtained directly from the commutation relations of these Lie algebras. To a considerable degree, the Lie algebraic approach unifies the theory of these special functions.

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