Abstract
The analysis of the asymptotic behavior of orthogonal polynomials was one of the driving forces for the resurgence of interest in potentials with external fields. The relationship between the two subjects can be seen as follows: consider, for example, orthogonal polynomials with respect to the so-called Freud weights W(x) = exp(-|x|λ) =: exp(-Q(x)). On applying the substitution x → n 1/λ x and the defining properties of orthogonal polynomials one arrives at monic polynomials P n minimizing the integral
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© 1997 Springer-Verlag Berlin Heidelberg
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Saff, E.B., Totik, V. (1997). Applications Concerning Orthogonal Polynomials. In: Logarithmic Potentials with External Fields. Grundlehren der mathematischen Wissenschaften, vol 316. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03329-6_8
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DOI: https://doi.org/10.1007/978-3-662-03329-6_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08173-6
Online ISBN: 978-3-662-03329-6
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