Application to the Binomial Summation of a Laplacian Method for the Evaluation of Definite Integrals
01 January 1929
T HE numerical evaluation of the incomplete Binomial Summation, a problem of major importance for many statistical and engineering applications of the Theory of Probability, is a question for which a satisfactory solution has not as yet been obtained. Several approximation formulas have been presented,2 each of which gives good results for some limited range of values of the variables involved; but a formula of wide applicability is still a desideratum. The purpose of this paper is to submit for consideration an approximation formula which seems to meet the situation to a measurable extent. The writer derived it by applying to the equation V (1)