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Letter from Jack Sherman to Linus Pauling. April 10, 1932.
Sherman writes to note that he and Ralph Hultgren have been working on the evaluation of Slater's "F" and "G" integrals and that he will send Pauling the results soon. Sherman will finish his thesis soon and would like Pauling's advice about obtaining a position for the next year if he does not get a fellowship with the National Research Council


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.



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