# in terms of elementary functions

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## 1—10 of 47 matching pages

##### 1: 9.19 Approximations

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###### §9.19(i) Approximations in Terms of Elementary Functions

…##### 2: 18.24 Hahn Class: Asymptotic Approximations

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►In particular, asymptotic formulas in terms of elementary functions are given when $z=x$ is real and fixed.
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►Dunster (2001b) provides various asymptotic expansions for ${C}_{n}(x;a)$ as $n\to \mathrm{\infty}$, in terms of elementary functions or in terms of Bessel functions.
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##### 3: 7.24 Approximations

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###### §7.24(i) Approximations in Terms of Elementary Functions

…##### 4: 6.20 Approximations

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###### §6.20(i) Approximations in Terms of Elementary Functions

…##### 5: 18.32 OP’s with Respect to Freud Weights

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►However, for asymptotic approximations in terms of elementary functions for the OP’s, and also for their largest zeros, see Levin and Lubinsky (2001) and Nevai (1986).
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##### 6: 12.10 Uniform Asymptotic Expansions for Large Parameter

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►With the upper sign in (12.10.2), expansions can be constructed for large $\mu $
in terms of elementary functions that are uniform for $t\in (-\mathrm{\infty},\mathrm{\infty})$ (§2.8(ii)).
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►The turning points can be included if expansions in terms of Airy functions are used instead of elementary functions (§2.8(iii)).
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###### §12.10(ii) Negative $a$, $$

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12.10.30
$${\overline{v}}_{s}(t)={\mathrm{i}}^{s}{v}_{s}(-\mathrm{i}t).$$

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###### §12.10(vi) Modifications of Expansions in Elementary Functions

…##### 7: 25.5 Integral Representations

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###### §25.5(i) In Terms of Elementary Functions

…##### 8: 33.20 Expansions for Small $|\u03f5|$

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►These expansions are in terms of elementary functions, Airy functions, and Bessel functions of orders $2\mathrm{\ell}+1$ and $2\mathrm{\ell}+2$.

##### 9: 28.8 Asymptotic Expansions for Large $q$

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►With additional restrictions on $z$, uniform asymptotic approximations for solutions of (28.2.1) and (28.20.1) are also obtained in terms of elementary functions by re-expansions of the Whittaker functions; compare §2.8(ii).
►Subsequently the asymptotic solutions involving either elementary or Whittaker functions are identified in terms of the Floquet solutions ${\mathrm{me}}_{\nu}(z,q)$ (§28.12(ii)) and modified Mathieu functions
${\mathrm{M}}_{\nu}^{(j)}(z,h)$ (§28.20(iii)).
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##### 10: 12.14 The Function $W(a,x)$

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