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Synopsis Explicit orthogonality relations are found for the associated Laguerre and Hermite polynomials. One consequence is the construction of the n − 1/ n Padé approximation to Ψ( a + 1, b ; x )/Ψ( a, b; x ), where Ψ( a, b; x ) is the second solution to the confluent hypergeometric differential equation that does not grow rapidly at infinity.
Askey et al. (Sun,) studied this question.