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Recurrence and Asymptotic Relations of a Generalized Elliptic-type Integral

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.