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Symmetries of 3n-j Coefficients and Generalized Hypergeometric Functions

In: Symmetries in Science X

Author

Listed:
  • K. Srinivasa Rao

    (The Institute of Mathematical Sciences)

Abstract

The 3n-jcoupling/recoupling angular momentum coefficients (for n= 1,2,3) are related to the generalized hypergeometric functions. The symmetries of these coefficients are then presented in terms of the inherent symmetries of the generalized hypergeometric functions. While the 3-j and the 6-jcoefficients are related to sets of 3 F 2(l)s and 4 F 3(1)s, respectively, the simplest known formula for the 9-jcoefficient is a triple sum series (due to Ališauskas, Jucys, and Bandzaitis) which has been related to a triple hypergeometric series, with unit arguments. From a novel way of looking at the symmetries of the 9-jcoefficient, we derive here the Bailey transform for a Saalschützian 4 F 3(1) and a transformation of a Kampé de Fériet function into a Saalschützian 4 F 3(1) or its Bailey transform.

Suggested Citation

  • K. Srinivasa Rao, 1998. "Symmetries of 3n-j Coefficients and Generalized Hypergeometric Functions," Springer Books, in: Bruno Gruber & Michael Ramek (ed.), Symmetries in Science X, pages 383-399, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-1537-5_24
    DOI: 10.1007/978-1-4899-1537-5_24
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