# asymptotic approximations to zeros

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## 1—10 of 67 matching pages

##### 1: 18.29 Asymptotic Approximations for $q$-Hahn and Askey–Wilson Classes

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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 $q$-Laguerre and continuous ${q}^{-1}$-Hermite polynomials see Chen and Ismail (1998).

##### 2: 13.22 Zeros

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►Asymptotic approximations to the zeros when the parameters $\kappa $ and/or $\mu $ are large can be found by reversion of the uniform approximations provided in §§13.20 and 13.21.
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##### 3: 10.74 Methods of Computation

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►Methods for obtaining initial approximations to the zeros include asymptotic expansions (§§10.21(vi)-10.21(ix)), graphical intersection of $2D$ graphs in $\mathbb{R}$ (e.
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##### 4: 5.4 Special Values and Extrema

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►As $n\to \mathrm{\infty}$,
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##### 5: 18.26 Wilson Class: Continued

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►For asymptotic expansions of Wilson polynomials of large degree see Wilson (1991), and for asymptotic approximations to their largest zeros see Chen and Ismail (1998).
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##### 6: 3.8 Nonlinear Equations

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►Initial approximations to the zeros can often be found from asymptotic or other approximations to
$f(z)$, or by application of the phase principle or Rouché’s theorem; see §1.10(iv).
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##### 7: 13.9 Zeros

###### §13.9 Zeros

… ► … ► … ► … ►For fixed $a$ and $z$ in $\u2102$, $U(a,b,z)$ has two infinite strings of $b$-zeros that are asymptotic to the imaginary axis as $|b|\to \mathrm{\infty}$.##### 8: 7.13 Zeros

###### §7.13 Zeros

… ►As $n\to \mathrm{\infty}$ … ►As $n\to \mathrm{\infty}$ the ${x}_{n}$ and ${y}_{n}$ corresponding to the zeros of $C\left(z\right)$ satisfy … ►In consequence of (7.5.5) and (7.5.10), zeros of $\mathcal{F}\left(z\right)$ are related to zeros of $\mathrm{erfc}z$. … ►##### 9: 36.15 Methods of Computation

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