A computing formula for the noncentral beta-distribution recently published by Nicholson is simplified. A table of figurate numbers is provided to facilitate the use of the simplified formula. It is compared for ease of use with the method of Tang in several situations.
J. L. Hodges Jr. "On the Noncentral Beta-Distribution." Ann. Math. Statist. 26 (4) 648 - 653, December, 1955. https://doi.org/10.1214/aoms/1177728424