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We find equivalent hypergeometric- and difference-equation-based formulas,$Q(k,\alpha)= G_1^k(\alpha) G_2^k(\alpha)$, for $k = -1, 0, 1,\ldots,9$, forthat (rational-valued) portion of the total separability probability forgeneralized two-qubit states endowed with random induced measure, for which thedeterminantal inequality $|\rho^{PT}| >|\rho|$ holds. Here $\rho$ denotes a $4\times 4$ density matrix and $\rho^{PT}$, its partial transpose, while $\alpha$is a Dyson-index-like parameter with $\alpha = 1$ for the standard(15-dimensional) convex set of two-qubit states. The dimension of the space inwhich these density matrices is embedded is $4 \times (4 +k)$. For thesymmetric case of $k=0$, we obtain the previously reported Hilbert-Schmidtformulas, with (the two-re[al]bit case) $Q(0,\frac{1}{2}) = \frac{29}{128}$,(the standard two-qubit case) $Q(0,1)=\frac{4}{33}$, and (thetwo-quater[nionic]bit case) $Q(0,2)= \frac{13}{323}$. The factors$G_2^k(\alpha)$ can be written as the sum of weighted hypergeometric functions$_{p}F_{p-1}$, $p \geq 7$, all with argument $\frac{27}{64} =(\frac{3}{4})^3$.We find formulas for the upper and lower parameter sets of these functions and,then, equivalently express $G_2^k(\alpha)$ in terms of first-order differenceequations. The factors $G_1^k(\alpha)$ are equal to$(\frac{27}{64})^{\alpha-1}$ times ratios of products of six Pochhammer symbolsinvolving the indicated parameters. Some remarkable $\alpha-$ and $k$-specificinvariant asymptotic properties (again, involving $\frac{27}{64}$ and relatedquantities) of separability probability formulas emerge.

Hypergeometric/Difference-Equation-Based Separability Probability  Formulas and Their Asymptotics for Generalized Two-Qubit States Endowed with  Random Induced Measure