Some properties of generalized secant integrals: extended definition and recurrence relations

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

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 (a0). 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.