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We analyze the asymptotic behavior of the sequences of monic polynomials that are orthogonal with respect to $w_{\\lambda}(x;t)$, as well as the asymptotic behavior of the recurrence coefficient, when the degree, or alternatively, the parameter $t$, tend to infinity. 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We analyze the asymptotic behavior of the sequences of monic polynomials that are orthogonal with respect to $w_{\\lambda}(x;t)$, as well as the asymptotic behavior of the recurrence coefficient, when the degree, or alternatively, the parameter $t$, tend to infinity. 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