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We compute the Harish-Chandra $c$-function for a generic class of rank-onepurely non-compact Riemannian symmetric superspaces $X=G/K$ in terms of Euler$\Gamma$ functions, proving that it is meromorphic. Compared to the even case,the poles of the $c$-function are shifted into the right half-space. We derivethe full asymptotic Harish-Chandra series expansion of the sphericalsuperfunctions on $X$. In the case where the multiplicity of the simple root isan even negative number, they have a closed expression as Jacobi polynomialsfor an unusual choice of parameters.

Asymptotics of spherical superfunctions on rank one Riemannian symmetric superspaces