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Symmetry 2010, 2(1), 346-365; doi:10.3390/sym2010345

Symmetry in Generating Functions

The University of Aizu, Ikki-machi Tsuruga, Aizu-Wakamatsu City, Fukushima 965-8580, Japan
Received: 23 February 2010 / Accepted: 16 March 2010 / Published: 19 March 2010
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
Download PDF [163 KB, 6 April 2010; original version 22 March 2010]


Generating functions play important roles in theory of orthogonal polynomials. In particular, it is important to consider generating functions that have symmetry. This paper is a survey on generating functions that define unitary operators. First, classical generating functions that define unitary operators are discussed. Next, group theoretical approach to generating functions that have unitarity are discussed.
Keywords: Generating function; Orthogonal polynomial; Zonal spherical function Generating function; Orthogonal polynomial; Zonal spherical function
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Watanabe, S. Symmetry in Generating Functions. Symmetry 2010, 2, 346-365.

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