Use of Padé Approximations in the Analytical Evaluation of the<i>J</i>(<i>θ,β</i>) Function and Its Temperature Derivative

Abstract

For the first time, analytical forms have been obtained for the finite resonance integral J(θ, β;x,1x2) defined by through the use of Padé approximations for the complex probability function. The analytical forms are in terms of elementary functions. We have investigated several 2-pole, 3-pole, and 4-pole Padé approximations, and of these, the 4-pole evaluation reproduces J(θ, β) with the best accuracy. We have also indicated how analytical forms for the temperature derivative of J(θ, β) may be obtained and discuss their utility.