error bounds

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21: Bibliography W

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Error bounds for asymptotic expansions of Hankel transforms. SIAM J. Math. Anal. 7 (6), pp. 799–808.

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External Links:

ISSN 1095-7154, Document, MathReview (John S. Lew), ZentralBlatt

Referenced by:

§10.22(v).

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Error bounds for asymptotic approximations of special functions. Ann. Numer. Math. 2 (1-4), pp. 181–197.

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Notes:

Special functions (Torino, 1993)

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ISSN 1021-2655, MathReview (Andrei Martínez Finkelshtein), ZentralBlatt

Referenced by:

§10.21(vi).

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22: 5.17 Barnes’ $G$-Function (Double Gamma Function)

… ►For error bounds and an exponentially-improved extension, see Nemes (2014a). …

23: Bibliography S

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On Lindelöf’s error bound for Stirling’s series. J. Reine Angew. Math. 404, pp. 135–139.

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External Links:

ISSN 0075-4102, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

§5.11(ii).

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Error bounds for a uniform asymptotic expansion of the Legendre function $P_n^{-m}(\cosh z)$ . Quart. Appl. Math. 46 (3), pp. 473–488.

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External Links:

ISSN 0033-569X, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§14.26.

Encodings:

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Error bounds for asymptotic solutions of differential equations. I. The distinct eigenvalue case. J. Res. Nat. Bur. Standards Sect. B 70B, pp. 167–186.

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External Links:

MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§2.7(ii).

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Error bounds for asymptotic solutions of differential equations. II. The general case. J. Res. Nat. Bur. Standards Sect. B 70B, pp. 187–210.

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External Links:

MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§2.7(ii).

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24: 7.12 Asymptotic Expansions

… ►For these and other error bounds see Olver (1997b, pp. 109–112), with $\alpha =\frac{1}{2}$ and $z$ replaced by $z^2$; compare (7.11.2). …

25: 11.11 Asymptotic Expansions of Anger–Weber Functions

… ►For sharp error bounds and exponentially-improved extensions, see Nemes (2018). … ►Error bounds for (11.11.8) and (11.11.10) are given in Meijer (1932) and Nemes (2014b, c). …

26: 13.20 Uniform Asymptotic Approximations for Large $\mu$

… ►For an extension of (13.20.1) to an asymptotic expansion, together with error bounds, see Olver (1997b, Chapter 10, Ex. 3.4). … ►This reference also supplies error bounds and corresponding approximations when $x$, $\kappa$, and $\mu$ are replaced by $\mathrm{i}x$, $\mathrm{i}\kappa$, and $\mathrm{i}\mu$, respectively. … ►Olver (1980b) also supplies error bounds and corresponding approximations when $x$, $\kappa$, and $\mu$ are replaced by $\mathrm{i}x$, $\mathrm{i}\kappa$, and $\mathrm{i}\mu$, respectively. …

27: 30.16 Methods of Computation

… ►Schäfke and Groh (1962) gives corresponding error bounds. …

28: Bibliography P

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Error bounds for the uniform asymptotic expansion of the incomplete gamma function. J. Comput. Appl. Math. 147 (1), pp. 215–231.

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External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§8.12.

Encodings:

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29: 8.12 Uniform Asymptotic Expansions for Large Parameter

… ►For error bounds for (8.12.7) see Paris (2002a). … ►Lastly, a uniform approximation for $\mathrm{\Gamma }(a,ax)$ for large $a$, with error bounds, can be found in Dunster (1996a). …

30: 14.15 Uniform Asymptotic Approximations

… ►For asymptotic expansions and explicit error bounds, see Dunster (2003b) and Gil et al. (2000). … ►For asymptotic expansions and explicit error bounds, see Dunster (2003b). … ►For asymptotic expansions and explicit error bounds, see Olver (1997b, Chapter 12, §§12, 13) and Jones (2001). … ►For asymptotic expansions and explicit error bounds, see Boyd and Dunster (1986). … ►For error bounds and other extensions see Olver (1975b). …