Abstract
Line sources with slab shields represent typical source–shield configurations in gamma-ray attenuation problems. Such shielding problems often lead to the generalized secant integrals of the form I a(ψ, b)=b a ∫ 0 ⥄⥄⥄⥄ψ e −b sec ϕ sec ϕ a dϕ, with b >0, 0< ψ⩽ π/2. Recently, the author has developed rapidly convergent infinite-series representation of generalized secant integrals involving incomplete gamma functions. The validity of this representation was established for zero and positive values of the integral parameter a ( a⩾0). In this paper the definition is extended to include negative real a values. It is demonstrated that the introduced series representation is still valid. In addition, general recurrence relations are established that allow precise calculation of the integral for negative a values.
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