Pasadena, Calif.

April 10, 1932

Dear Linus

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.

Sincerely,

Jack

Pasadena, Calif.

April 18, 1932

Dear Linus,

I am enclosing the formulae which Ralph and I obtained for the "F" and "G" integrals. As you can readily see, the formulae are quite complex due to the term containing the quintuple summation. By algebraic manipulation it may be possible to considerably simplify the formulae. However, Ralph and I have decided to postpone doing any further work on the problem. He wishes to devote all his time to studying for the doctorate examination and I wish to devote all my time to completing my thesis. We hope to continue about the beginning of June.

Last Friday and Saturday Cal Tech held its annual exhibit day. While I was setting up the crystal structure exhibit on Thursday a "Star-News" photographer came in the room and insisted on taking the picture which I am enclosing.

I hope that you and Mrs. Pauling are having a most enjoyable time. I want you to express my appreciation to Mrs. Pauling for her kind note thanking me for the box of candy which I presented to you both.

I shall appreciate any comments which you may make concerning the formulae.

Sincerely,

Jack