in terms of elementary functions

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1: 9.19 Approximations

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§9.19(i) Approximations in Terms of Elementary Functions

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2: 18.24 Hahn Class: Asymptotic Approximations

… ►In particular, asymptotic formulas in terms of elementary functions are given when $z=x$ is real and fixed. … ►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. …

3: 7.24 Approximations

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§7.24(i) Approximations in Terms of Elementary Functions

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4: 6.20 Approximations

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§6.20(i) Approximations in Terms of Elementary Functions

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5: 18.32 OP’s with Respect to Freud Weights

… ►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). …

6: 12.10 Uniform Asymptotic Expansions for Large Parameter

… ►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)). … ►The turning points can be included if expansions in terms of Airy functions are used instead of elementary functions (§2.8(iii)). … ►

§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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Defines:

${\overline{v}}_s(t)$: solution (locally)

Symbols:

$\mathrm{i}$: imaginary unit, $s$: nonnegative integer and $v_s(t)$: solution

Permalink:

http://dlmf.nist.gov/12.10.E30

Encodings:

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See also:

Annotations for §12.10(v), §12.10 and Ch.12

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§12.10(vi) Modifications of Expansions in Elementary Functions

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7: 25.5 Integral Representations

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§25.5(i) In Terms of Elementary Functions

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8: 33.20 Expansions for Small $|ϵ|$

… ►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 $q$

… ►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)). …

10: 12.14 The Function $W(a,x)$

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Positive $a$,

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