SUMMATION OF A FINITE SERIES OCCURRING IN KILL PROBABILITY FOR A CIRCULAR TARGET ENGAGED BY A SALVO OF AREA KILL WEAPONS

The probability function expressing the fractional kill of a circular target engaged by a salvo of area kill weapons can be expressed in terms of a finite series. When the salvo contains many rounds, the nature of the series makes it useless in computing the kill probability. In cases where the distribution of hits is bivariate normal, with equal or near equal standard deviations, this difficulty may be overcome by expressing the series in terms of a definite integral, readily solved by numerical quadrature. Additionally, the definite integral is expressed in terms of a different finite series having properties making it easily summable on a digital computer.