Some families of generalized elliptic-type integrals

The object of the present paper is first to point out a hitherto unnoticed relationship between two seemingly different families of generalized elliptic-type integrals which were studied recently. This relationship and some other simple techniques are then employed in order to derive many properties (including, for example, analytic continuations and asymptotic behaviors) of these families. Several interesting special cases, involving simpler elliptic-type integrals, are also considered.