Abstract
The Bailey transform for a Saalschutzian4F3(1) and a transformation of aKampe de Feriet function into a Saalschutzian4F3(1) or its Bailey transform arederived in a novel way in this article: from the simplest known formula for the 9-j coefficient,due to Alisauskas–Jucys–Bandzaitis, which isthe triple sum series. It becomes a single, double, or(remains a) triple series when one of the angularmomenta is set to zero, due to its inherent lack ofsymmetry. This then is equated to a4F3(1) representation of the 6-jcoefficient to which the 9-j coefficient reduces whenany one of the nine angular momenta is zero.
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REFERENCES
Ališuskas, S. J., and Jucys, A. P. (1971). Journal of Mathematical Physics, 12, 594.
Biedenharn, L. C., and Louck, J. D. (1981). The Racah—Wigner Algebra in Quantum Theory, Encyclopedia of Mathematics and Its Applications, Vol. 9, Academic Press, New York.
Edmonds, A. R. (1957). Angular Momentum in Quantum Mechanics, Princeton University Press, Princeton, New Jersey.
Jucys, A. P., and Bandzaitis, A. A. (1977). Angular Momentum in Quantum Physics, Mokslas, Vilnius, Lithuania.
Karlsson, P. W. (1994). Journal of Physics A, 27, 6943.
Lauricella, G. (1893). Rendiconti del Circolo Matematico di Palermo, 1, 111.
Minton, B. M. (1970). Journal of Mathematical Physics, 11, 1375.
Pitre, S. N., and Van der Jeugt, J. (1996). Journal of Mathematical Analysis and Applications, 202, 121.
Saran, S. (1954). Ganita, 5, 77; Addendum, ibid. (1956) 7, 65.
Slater, L. J. (1966). Generalized Hypergeometric Functions, Cambridge University Press, Cambridge.
Srinivasa Rao, K., and Rajeswari, V. (1989). Journal of Mathematical Physics, 30, 1016.
Srinivasa Rao, K., and Rajeswari, V. (1993). Quantum Theory of Angular Momentum: Selected Topics, Springer, Berlin, and Narosa, Delhi.
Srinivasa Rao, K., and Venkatesh, K. (1977). In Group Theoretical Methods in Physics, Proceedings of the Vth International Colloquium, University of Montreal, Sharp, R. T., and Kolman, B., eds., Academic Press, New York, p. 649.
Srinivasa Rao, K., Rajeswari, V., and Chiu, C. B. (1989). Computer Physics Communications, 56, 231.
Srinivasa Rao, K., Santhanam, T. S., and Venkatesh, K. (1975). Journal of Mathematical Physics, 16, 1528.
Srivastava, H. M. (1964). Ganita, 15, 97.
Srivastava, H. M., and Daoust, M. C. (1969). Proceedings of the Nederlandse Akademie der Wetenschappen A, 72, 449.
Van der Jeugt, J., Pitre, S. N., and Srinivasa Rao, K. (1994). Journal of Physics A, 27, 5251.
Varshalovich, D. A., Moskalev, A. N., and Khersonskii, V. K. (1975). Quantum Theory of Angular Momentum, Nauka, Leningrad [in Russian; English translation, 1988 World Scientific, Singapore].
Vilenkin, N. Ja., and Klimyk, A. U. (1991). Representations of Lie Groups and Special Functions, Vol. 1, Kluwer, Dordrecht.
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Srinivasa, K., Van Der Jeugt, R.J. Transformations of Single and Double Hypergeometric Series from the Triple Sum Series for the 9-j Coefficient. International Journal of Theoretical Physics 37, 891–905 (1998). https://doi.org/10.1023/A:1026632900221
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DOI: https://doi.org/10.1023/A:1026632900221