Calculation of generalized Hubbell rectangular source integral

TL;DR

This paper introduces a simple formula for calculating the generalized Hubbell rectangular source integral, providing a practical approximation method and numerical comparisons with existing results.

Contribution

The paper presents a new approximation formula for the generalized Hubbell integral and validates it through numerical tables comparing with previous literature.

Findings

The formula accurately approximates the integral.

Numerical tables demonstrate close agreement with established results.

The method simplifies computation of the integral.

Abstract

A simple formula for computing the generalized Hubbell radiation rectangular source integral $$H[{a,b,p,\lambda \atop \alpha,\beta,\gamma}]=\frac{\sigma a}{4\pi}\int_0^b x^\lambda(x^2+p)^{-\alpha}{}_2F_1(\alpha,\beta;\gamma;-{a^2\over x^2+p})dx, $$ is introduced. Tables are given to compare the numerical values derived from our approximation formula with those given earlier in the literature.