ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
It is shown that Thomae's identity between two 3F2 hypergeometric series of unit argument together with the trivial invariance under separate permutations of numerator and denominator parameters implies that the symmetric group S5 is an invariance group of this series. A similar result is proved for the terminating Saalschützian 4F3 series, where S6 is shown to be the invariance group of this series (or S5 if one parameter is eliminated by using the Saalschütz condition). Here Bailey's identity is realized as a permutation of appropriately defined parameters. Finally, the set of three-term relations between 3F2 series of unit argument discovered by Thomae [J. Thomae, J. Reine Angew. Math. 87, 26 (1879)] and systematized by Whipple [F. J. Whipple, Proc. London Math. Soc. 23, 104 (1925)] is shown to be transformed into itself under the action of the group S6×Λ, where Λ is a two-element group. The 12 left cosets of S6×Λ with respect to the invariance group S5 are the structural elements underlying the three-term relations. The symbol manipulator macsyma was used to obtain preliminary results.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.527634
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