Recurrence and Asymptotic Relations of a Generalized Elliptic-type Integral
نویسنده
چکیده
Epstein-Hubbell 1963 elliptic-type integrals occur in radiation field problems. In this paper, we consider a generalization of the elliptic-type integrals introduced by Kalla and Tuan 1996 and developed by Salman 2006. We give some recurrence relations for this generalized special function. Some of these relations can be used for analytic continuation to different domains. Asymptotic relations of the generalized function are constructed at one of its singular points. These relations are derived by using some of the analytic continuation formulas of the related Gauss hypergeometric function. Introduction Elliptic integrals (Abramowitz and Stegun, 1972; Byrd and Friedman, 1971; Evans et al., 1993; Kaplan, 1950) occur in a number of physical problems. Epstein and Hubbell 1963 have treated the elliptic-type integrals
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