LEGENDRE EXPANSION RELATED TO THE HUBBELL RECTANGULAR SOURCE INTEGRAL

摘要

A Legendre odd-powers polynomial expansion of arctan(x) is derived for use in solving the Hubbell Rectangular Source Integral ∫_0~b 1/(β~2+1)~(1/2) arctan (a/(β~2+1)~(1/2) dβ. As the result, two rapidly convergent series for Hubbell integral are produced; one for a/(β~2+1)~(1/2) > 1. An upper bound of the absolute error of approximation is such that assures rapid improvement of accuracy for every additional term of the series.