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1: 15.12 Asymptotic Approximations

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§15.12(ii) Large $c$

… ►For large $b$ and $c$ with $c>b+1$ see López and Pagola (2011). … ►As $\lambda \to \mathrm{\infty }$, … ►If , then as $\lambda \to \mathrm{\infty }$ with $|\mathrm{ph}\lambda |\le \pi -\delta$, … ►For other extensions, see Wagner (1986), Temme (2003) and Temme (2015, Chapters 12 and 28).

2: Bibliography F

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The third Appell function for one large variable. J. Approx. Theory 165, pp. 60–69.

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External Links:

ISSN 0021-9045, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§16.13, §16.13.

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Incomplete gamma functions for large values of their variables. Adv. in Appl. Math. 34 (3), pp. 467–485.

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External Links:

ISSN 0196-8858, Document, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§8.12.

Encodings:

BibTeX

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The second Appell function for one large variable. Mediterr. J. Math. 10 (4), pp. 1853–1865.

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External Links:

ISSN 1660-5446, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§16.13, §16.13.

Encodings:

BibTeX

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Uniform asymptotic expansions of certain classes of Meijer $G$-functions for a large parameter. SIAM J. Math. Anal. 4 (3), pp. 482–507.

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External Links:

Document, MathReview (C. M. Joshi), ZentralBlatt

Referenced by:

§16.22.

Encodings:

BibTeX

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3: 28.26 Asymptotic Approximations for Large $q$

§28.26 Asymptotic Approximations for Large $q$

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§28.26(ii) Uniform Approximations

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4: 28.25 Asymptotic Expansions for Large $\mathrm{\Re }z$

§28.25 Asymptotic Expansions for Large $\mathrm{\Re }z$

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5: Bibliography H

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On the resurgence properties of the uniform asymptotic expansion of Bessel functions of large order. Proc. Roy. Soc. London Ser. A 455, pp. 3917–3930.

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External Links:

ISSN 1364-5021, Document, MathReview (A. D. Wood), ZentralBlatt

Referenced by:

§10.20(ii).

Encodings:

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6: 28.34 Methods of Computation

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Use of asymptotic expansions for large $z$ or large $q$. See §§28.25 and 28.26.

7: 6.18 Methods of Computation

… ► $A_0$, $B_0$, and $C_0$ can be computed by Miller’s algorithm (§3.6(iii)), starting with initial values $(A_N,B_N,C_N)=(1,0,0)$, say, where $N$ is an arbitrary large integer, and normalizing via $C_0=1/z$. …

8: Bibliography B

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C Mathematical Function Handbook. McGraw-Hill, Inc., New York.

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Notes:

Includes diskette containing a large collection of mathematical function software written in C; Double-precision, maximum accuracy 9S.

External Links:

ISBN 00-791-1158-0

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

Encodings:

BibTeX

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Anharmonic oscillator. II. A study of perturbation theory in large order. Phys. Rev. D 7, pp. 1620–1636.

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External Links:

Document

Referenced by:

§22.19(ii).

Encodings:

BibTeX

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Coulomb functions for large charges and small velocities. Phys. Rev. (2) 97 (2), pp. 542–554.

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External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§33.5(iv).

Encodings:

BibTeX

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9: Bibliography J

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Derivation of Green-type, transitional and uniform asymptotic expansions from differential equations. V. Angular oblate spheroidal wavefunctions ${\overline{ps}}_n^r(\eta ,h)$ and ${\overline{qs}}_n^r(\eta ,h)$ for large $h$ . Proc. Roy. Soc. London Ser. A 321, pp. 545–555.

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External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§30.9(ii).

Encodings:

BibTeX

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10: 15.19 Methods of Computation

… ►Initial values for moderate values of $|a|$ and $|b|$ can be obtained by the methods of §15.19(i), and for large values of $|a|$, $|b|$, or $|c|$ via the asymptotic expansions of §§15.12(ii) and 15.12(iii). ►For example, in the half-plane $\mathrm{\Re }z\le \frac{1}{2}$ we can use (15.12.2) or (15.12.3) to compute $F(a,b;c+N+1;z)$ and $F(a,b;c+N;z)$, where $N$ is a large positive integer, and then apply (15.5.18) in the backward direction. …