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►In the recurrence relation (18.2.8) assume that the coefficients , , and are defined when is a continuous nonnegative real variable, and let be an arbitrary positive constant.
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►
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►Ismail (1986) gives asymptotic expansions as , with and other parameters fixed, for continuous
-ultraspherical, big and little -Jacobi, and Askey–Wilson polynomials.
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►For a uniform asymptotic expansion of the Stieltjes–Wigert polynomials, see Wang and Wong (2006).
►For asymptotic approximations to the largest zeros of the -Laguerre and continuous
-Hermite polynomials see Chen and Ismail (1998).
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►Koornwinder (2009) rescales and reparametrizes Racah polynomials and Wilson polynomials in such a way that they are continuous in their four parameters, provided that these parameters are nonnegative.
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►Table 18.25.1 lists the transformations of variable, orthogonality ranges, and parameter constraints that are needed in §18.2(i) for the Wilson polynomials , continuous dual Hahn polynomials , Racah polynomials , and dual Hahn polynomials .
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►
§18.25(ii) Weights and Normalizations: Continuous Cases
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►From the mathematical standpoint the left-hand side of (1.17.2) can be interpreted as a generalized integral in the sense that
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►for all functions that are continuous when , and for each , converges absolutely for all sufficiently large values of .
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►More generally, assume is piecewise continuous (§1.4(ii)) when for any finite positive real value of , and for each , converges absolutely for all sufficiently large values of .
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►provided that is continuous when , and for each , converges absolutely for all sufficiently large values of (as in the case of (1.17.6)).
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►provided that is continuous and of period ; see §1.8(ii).
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