Asymptotic expansions of the generalized Epstein-Hubbell integral

The generalized Epstein–Hubbell integral recently introducedby Kalla & Tuan (Comput. Math. Applic. 32, 1996) is consideredfor values of the variable k close to its upper limit k = 1.Distributional approach is used for deriving two convergentexpansions of this integral in increasing powers of 1 –k². For certain values of the parameters, one of these expansionsinvolves also a logarithmic term in the asymptotic variable1 – k². Coefficients of these expansions are given interms of the Appell function and its derivative. All the expansionsare accompanied by an error bound at any order of the approximation.Numerical experiments show that this bound is considerably accurate.