Evaluation of the Hubbell Radiation Rectangular Source Integral Using Binomial Coefficients

Abstract

Using binomial coefficients a general series expansion formula is established for the integral I<inf>q</inf>(a,b)=∫0a1(1+b2+x 2)q dx with integer and noninteger values of q appearing in the evaluation of the radiation field generated by a plane isotropic rectangular source (plaque). With the help of this relation the Hubbell radiation rectangular source (HRS) integrals (J. Res. 64C(2) (1960) 121; Appl. Radiat. Isot. 39 (1988) 421) are calculated. The convergence of the series is tested by the concrete cases for values b and a. These formulae are especially useful for the calculation of HRS integrals for small values b and a. © 2003 Elsevier Ltd. All rights reserved.