Calculation of generalized Hubbell rectangular source integral

preprint2010arXivOpen access

Abstract

A simple formula for computing the generalized Hubbell radiation rectangular source integral H[a,b,p,λα,β,γ]=σa4π∫0bxλ(x2+p)−α2F1(α,β;γ;−a2x2+p)dx,H[{a,b,p,λ\atop α,β,γ}]=\frac{σa}{4π}\int_0^b x^λ(x^2+p)^{-α}{}_2F_1(α,β;γ;-{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.

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