Development of the Hubbell Rectangular Source Integral

Author: Kalla S.L.  

Publisher: Springer Publishing Company

ISSN: 0167-8019

Source: Acta Applicandae Mathematicae, Vol.74, Iss.1, 2002-10, pp. : 35-55

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Abstract

The integral \[\int_{0}^{b}\frac{1}{\sqrt{x^{2}+1}}\,\tan^{-1}\biggl[\frac{a}{\sqrt{x^{2}+1}} \biggr]\,\mathrm{d}x\] is the leading term in a series solution appearing in the computation of the radiation field from a plane isotropic rectangular source, and is known as the ‘Hubbell Rectangular Source Integral’ – HRSI. A survey of various properties of HRSI, namely its series representations, asymptotic formulas, recurrence relations and approximation formulas, as well as some previous generalizations is presented here. In addition, a further generalization of HRSI using a modified form of the Gauss hypergeometric function is proposed.