study will follow the work of Dr Clare Dunning and Professor Peter Clarkson on orthogonal polynomials and special functions.

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Wronskian polynomials play a key role in certain solutions of the Painleve equations. The results have a multitude of applications, for example vortex dynamics, supersymmetric quantum mechanics, and solutions of the de-focusing nonlinearSchrodinger equation [6]. An overview of the applications of Wronskian Hermitepolynomials is provided in [1], including the theory of exceptional orthogonal polynomials, quantum harmonic oscillators, certain integrable massless quantum fieldtheory, and more. Applications of Wronskian polynomials motivates the need forfuture studies of their properties.