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A new symmetry for Biedenharn's G-functions and classical hypergeometric series

✍ Scribed by R.A Gustafson; S.C Milne

Publisher: Elsevier Science
Year: 1985
Tongue: English
Weight: 639 KB
Volume: 57
Category: Article
ISSN: 0001-8708
DOI: 10.1016/0001-8708(85)90063-5

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✦ Synopsis

We show that the general bisymmetric polynomials ;Gf)(y,,..., y,,; a,,..., 6,) are a limiting case of the bisymmetric, invariant polynomials ;Grr(y,,...,y,; a,,..., 6,) which characterize U(n) tensor operators (p, q,..., q. 0, . . . . 0). By taking suitable limits of a pair of difference equations for ;G$"(y; 6) we then deduce "transposition symmetry" for ;GF)(y; S) from the same symmetry for ;Gr)(y; 6). As an application of transposition symmetry for ;Gr)(y; 6) we derive an elegant, new contiguous relation for classical, well-poised hypergeometric series, and also prove an identity between these series and multiple hypergeometric series well-poised in Su(n). f(T) 1985 Academic Press, Inc.

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