DOI QR코드

DOI QR Code

ON SUMMATION THEOREMS FOR THE 3F2(1) SERIES

Rao, K. Srinivasa;Suresh, R.

  • 발행 : 2009.11.30

초록

The intimate relation between the 3-j coefficient in Quantum Theory of Angular Momentum (QTAM) and the $_3F_2(1)$ hypergeometric series is exploited to derive new summation theorems, from formulas for the 3-j coefficient.

키워드

angular momentum coupling coefficient;Clebsch-Gordan coefficient;generalized hypergeometric series

참고문헌

  1. B. C. Berndt, Ramanujan's Notebooks, Part I to V, Springer, New York, (1985)-(2005)
  2. L. C. Biedenharn and J. D. Louck, Angular Momentum in Quantum Physics, Theory and application. With a foreword by Peter A. Carruthers. Encyclopedia of Mathematics and its Applications, 8. Addison-Wesley Publishing Co., Reading, Mass., 1981
  3. G. S. Carr, Formulas and Theorems in Pure Mathematics, Second edition. With an introduction by Jacques Dutka. Chelsea Publishing Co., New York, 1970
  4. A. R. Edmonds, Angular Momentum in Quantum Mechanics, Princeton University Press, 1957
  5. S. Ramanujan, Notebooks of Srinivasa Ramanujan, facsimile edition, published by the Tata Institute of Fundamental Research, Mumbai (1957), two volumes
  6. T. Regge, Nuovo Cimento 11 (1959), 116 https://doi.org/10.1007/BF02724914
  7. M. E. Rose, Elementary Theory of Angular Momentum, John Wiley & Sons, New York, 1957
  8. L. J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, 1966
  9. Ya. A. Smorodinskii and L. A. Shelepin, Clebsch-Gordan coefficients, viewed from different sides, Soviet Physics Uspekhi 15 (1972), 1-24.; translated from Uspehi Fiz Nauk 106 (1972), 3-45
  10. K. Srinivasa Rao and V. Rajeswari, Quantum Theory of Angular Momentum. Selected Topics, Springer-Verlag, Berlin; Narosa Publishing House, New Delhi, 1993
  11. K. Srinivasa Rao, G. Vanden Berghe, and C. Krattenthaler, An entry of Ramanujan on hypergeometric series in his notebooks, J. Comput. Appl. Math. 173 (2005), no. 2, 239-246 https://doi.org/10.1016/j.cam.2004.03.009
  12. F. J. W. Whipple, A group of generalized hypergeometric series: relations between 120 allied series of the type F[a, b, c; d, e], Proc. London Math. Soc. (2) 23 (1925), 104-114 https://doi.org/10.1112/plms/s2-23.1.104
  13. J. Van der Jeugt, S. N. Pitre, and K. Srinivasa Rao, Transformation and summation formulas for double hypergeometric series, J. Comput. Appl. Math. 83 (1997), no. 2, 185-193 https://doi.org/10.1016/S0377-0427(97)00096-4
  14. M. E. Rose, Multipole Fields, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1955
  15. K. Srinivasa Rao, J. Van der Jeugt, J. Raynal, R. Jagannathan, and V. Rajeswari, Group theoretical basis for the terminating $_3F_2(1)$ series, J. Phys. A 25 (1992), no. 4, 861-876 https://doi.org/10.1088/0305-4470/25/4/023