Polynomial Solutions of Brioschi-Halphen Equation

Unanaowo Nyong Bassey, Ubong Sam Idiong

Abstract


In this paper, we give point canonical transformations (PCT) which map the Brioschi Halphen equation (BHE) into differential equations of complex classical orthogonal polynomials. We also construct exactly solvable potentials, without supersymmetry or factorization and the concept of shape invariance, which give rise to the solutions of the BHE which may be expressed in terms of complex Jacobi polynomials, Laguerre polynomials and Hermite polynomials.

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References


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