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.