asymptotic approximations for large order

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1: 14.26 Uniform Asymptotic Expansions

§14.26 Uniform Asymptotic Expansions

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2: 10.57 Uniform Asymptotic Expansions for Large Order

§10.57 Uniform Asymptotic Expansions for Large Order

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3: 14.15 Uniform Asymptotic Approximations

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§14.15(i) Large $\mu$, Fixed $\nu$

… ►For asymptotic expansions and explicit error bounds, see Dunster (2003b). …

4: 10.41 Asymptotic Expansions for Large Order

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§10.41(iv) Double Asymptotic Properties

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§10.41(v) Double Asymptotic Properties (Continued)

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5: 14.20 Conical (or Mehler) Functions

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§14.20(ix) Asymptotic Approximations: Large $\mu$, $0\le \tau \le A\mu$

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6: 10.21 Zeros

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§10.21(viii) Uniform Asymptotic Approximations for Large Order

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7: 10.69 Uniform Asymptotic Expansions for Large Order

§10.69 Uniform Asymptotic Expansions for Large Order

… ►All fractional powers take their principal values. ►All four expansions also enjoy the same kind of double asymptotic property described in §10.41(iv). … ►

8: 15.12 Asymptotic Approximations

§15.12 Asymptotic Approximations

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§15.12(i) Large Variable

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§15.12(ii) Large $c$

… ►As $\lambda \to \mathrm{\infty }$, … ►For other extensions, see Wagner (1986), Temme (2003) and Temme (2015, Chapters 12 and 28).

9: 10.72 Mathematical Applications

… ►Then for large $u$ asymptotic approximations of the solutions $w$ can be constructed in terms of Bessel functions, or modified Bessel functions, of variable order (in fact the order depends on $u$ and $\alpha$). …

10: 34.8 Approximations for Large Parameters

§34.8 Approximations for Large Parameters

►For large values of the parameters in the $\mathit{3}j$, $\mathit{6}j$, and $\mathit{9}j$ symbols, different asymptotic forms are obtained depending on which parameters are large. … ►Semiclassical (WKBJ) approximations in terms of trigonometric or exponential functions are given in Varshalovich et al. (1988, §§8.9, 9.9, 10.7). Uniform approximations in terms of Airy functions for the $\mathit{3}j$ and $\mathit{6}j$ symbols are given in Schulten and Gordon (1975b). For approximations for the $\mathit{3}j$, $\mathit{6}j$, and $\mathit{9}j$ symbols with error bounds see Flude (1998), Chen et al. (1999), and Watson (1999): these references also cite earlier work.