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11: Bibliography E

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The asymptotic behaviour of the inhomogeneous Airy function $\mathrm{Hi}(z)$ . Math. Chronicle 12, pp. 99–104.

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External Links:

ISSN 0581-1155, MathReview (Ram Kishore Saxena), ZentralBlatt

Referenced by:

(9.12.24), §9.12(vii).

Encodings:

BibTeX

12: Bibliography K

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Two new asymptotic methods in the theory of wave propagation in inhomogeneous media. Sov. Phys. Acoust. 14, pp. 1–17.

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External Links:

ISSN 0038-562X

Referenced by:

§36.14(iv).

Encodings:

BibTeX

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Quantum-Theoretical Formalism for Inhomogeneous Graded-Index Waveguides. Akademie Verlag, Berlin-New York.

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External Links:

ISBN 3-05-501598-3, MathReview (Apostolos Vourdas), ZentralBlatt

Referenced by:

§10.73(i).

Encodings:

BibTeX

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13: Bibliography O

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On higher-order Stokes phenomena of an inhomogeneous linear ordinary differential equation. J. Comput. Appl. Math. 169 (1), pp. 235–246.

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External Links:

ISSN 0377-0427, Document, MathReview (Jorge Mozo Fernández), ZentralBlatt

Referenced by:

§2.11(iv).

Encodings:

BibTeX

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14: 11.10 Anger–Weber Functions

… ►The Anger and Weber functions satisfy the inhomogeneous Bessel differential equation …

15: 10.15 Derivatives with Respect to Order

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16: Bibliography G

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On nonoscillating integrals for computing inhomogeneous Airy functions. Math. Comp. 70 (235), pp. 1183–1194.

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External Links:

Document, MathReview (Richard B. Paris), ZentralBlatt

Referenced by:

§3.5(ix), §9.17(iii).

Encodings:

BibTeX

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17: Bibliography L

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The inhomogeneous Airy functions, $\mathrm{Gi}(z)$ and $\mathrm{Hi}(z)$ . J. Chem. Phys. 72 (1), pp. 332–336.

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External Links:

ISSN 0021-9606, Document, MathReview (V. L. Deshpande)

Referenced by:

(9.12.21), §9.12(vii), §9.17(iii).

Encodings:

BibTeX

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18: 11.11 Asymptotic Expansions of Anger–Weber Functions

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11.11.17 $${𝐀}_{-\nu }\left(\nu +a{\nu }^{1/3}\right)=2^{1/3}{\nu }^{-1/3}\mathrm{Hi}\left(-2^{1/3}a\right)+O\left({\nu }^{-1}\right),$$

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Symbols:

$O\left(x\right)$: order not exceeding, $\mathrm{Hi}\left(z\right)$: Scorer function (inhomogeneous Airy function), ${𝐀}_{\nu }\left(z\right)$: Anger–Weber function, $\nu$: real or complex order and $a_k(\lambda )$: expansion function

Sources:

Olver (1997b, pp. 103 and 352); Nemes (2020)

Referenced by:

§11.11(iii), §11.11(iii), §11.11(iii)

Permalink:

http://dlmf.nist.gov/11.11.E17

Encodings:

pMML, png, TeX

See also:

Annotations for §11.11(iii), §11.11 and Ch.11

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19: 2.8 Differential Equations with a Parameter

… ►For error bounds, extensions to pure imaginary or complex $u$, an extension to inhomogeneous differential equations, and examples, see Olver (1997b, Chapter 10). … ►For error bounds, more delicate error estimates, extensions to complex $\xi$ and $u$, zeros, connection formulas, extensions to inhomogeneous equations, and examples, see Olver (1997b, Chapters 11, 13), Olver (1964b), Reid (1974a, b), Boyd (1987), and Baldwin (1991). …

20: Bibliography B

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Coefficient functions for an inhomogeneous turning-point problem. Mathematika 38 (2), pp. 217–238.

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External Links:

ISSN 0025-5793, MathReview (Archibald D. MacGillivray), ZentralBlatt

Referenced by:

§2.8(iii).

Encodings:

BibTeX

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