April 10, 1932
During the past week Hultgren and I have been working on the evaluation of Slater's "F" and "G" integrals. By making use of
the generating function of the associated Laguerre polynomial we obtain a result for the "F" integral involving only one term,
but this term involves a triple summation, one of the summations going from zero to infinity. Although this result is undoubtedly
correct, the fact that it is an infinite series is a decided disadvantage practically. By expressing the associated Laguerre
polynomial in polynomial form and not using the generating function at all, we are led to a result for the "F" and "G" integrals
involving only finite summations.
The expression for the "F" integral consists of the sum of two terms, one term involving a quadruple summation, the other
term involving a quintuple summation. The four summations are between the limits 0 and n - l -1.
For the particular case when l = n - 1, the expression for "F" is particularly simple, involving only a single summation.
However, when xxxx l ~ n - 2, n - 3, etc. the expression for "F" increases enormously in complexity. The results which we
have obtained are undoubtedly correct, since I am able to check the answers which I obtained in the special cases (in the
term report which you have). As soon as we amplify our results I shall send you a complete description of them.
I hope that you and Mrs. Pauling have had a very enjoyable trip across the country.
I hope to have my thesis completely written by the end of this month, and I shall send you a copy as soon as it is completed.
I am anxiously awaiting the results of the fellowship awards of the National Research Council. If I do not get a fellowship,
I don't know what I am going to do. I shall greatly appreciate any suggestions which you can give to me as to other possibilities
of obtaining a position for next year.
I hope that you are having an enjoyable time at M.I.T. I hope to hear from you soon.