Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-25T01:08:11.391Z Has data issue: false hasContentIssue false
  • English
  • Français

Simple proof of a formula due to Racah

Published online by Cambridge University Press:  24 October 2008

J. S. Griffith
J. S. Griffith
Affiliation:
Department of Theoretical Chemistry, University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Extract

After some manipulation from the general formula, Racah (1,2) obtained a closed formula for his V coefficient in the special case of all three mj- components zero. He also showed that the integral of the product of three Legendre polynomials followed at once from these special V coefficients. In this case the general formula ((2), eq. 10–14) becomes

where

and a, b, c are all non-negative integers. By changing the parameter of summation to (a+ b−c−p) it follows that is zero unless 2g = a+b+c is even (2).

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 2 , April 1963 , pp. 507
Copyright
Copyright © Cambridge Philosophical Society 1963

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Racah, G.Phys. Rev. 62 (1942), 438.CrossRefGoogle Scholar
(2)Fano, U., and Racah, G., Irreducible tensorial sets (Academic Press, 1959).Google Scholar
(3)Fjeldstad, J. E., Math. Scand. 2 (1954), 46.CrossRefGoogle Scholar
(4)Good, I. J., Proc. Cambridge Philos. Soc. 58 (1962), 161.CrossRefGoogle Scholar