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The limiting set of zeros of generalized Bessel polynomials with varyingparameters depending on the degree n cluster in a curve on the complex plane,which is a finite critical trajectory of a quadratic differential in the form{\lambda}^2(((z-a)(z-b))/(z^4))dz^2. The motivation of this paper is thedescription of the critical graphs of these quadratic differentials. Inparticular, we give a necessary and sufficient condition on the existence ofshort trajectories.

Algebraic equation and quadratic differential related to generalized Bessel polynomials with varying parameters