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11: 11.14 Tables

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Zhang and Jin (1996) tabulates ${𝐇}_n\left(x\right)$ and ${𝐋}_n\left(x\right)$ for $n=-4(1)3$ and $x=0(1)20$ to 8D or 7S.

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§11.14(iv) Anger–Weber Functions

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Bernard and Ishimaru (1962) tabulates ${𝐉}_{\nu }\left(x\right)$ and ${𝐄}_{\nu }\left(x\right)$ for $\nu =-10(.1)10$ and $x=0(.1)10$ to 5D.

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§11.14(v) Incomplete Functions

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Agrest and Maksimov (1971, Chapter 11) defines incomplete Struve, Anger, and Weber functions and includes tables of an incomplete Struve function ${𝐇}_n\left(x,\alpha \right)$ for $n=0,1$, $x=0(.2)10$, and $\alpha =0(.2)1.4,\frac{1}{2}\pi$, together with surface plots.

12: 11.11 Asymptotic Expansions of Anger–Weber Functions

§11.11 Asymptotic Expansions of Anger–Weber Functions

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§11.11(i) Large $|z|$, Fixed $\nu$

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§11.11(ii) Large $|\nu |$, Fixed $z$

… ►If $\nu =n(\in \mathbb{Z})$, then (11.10.29) applies for ${𝐉}_n\left(z\right)$, and …

13: 10.35 Generating Function and Associated Series

… ►Jacobi–Anger expansions: for $z,\theta \in ℂ$, …

14: Bibliography N

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On an integral transform involving a class of Mathieu functions. SIAM J. Math. Anal. 20 (6), pp. 1500–1513.

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External Links:

ISSN 0036-1410, Document, MathReview (K. C. Gupta), ZentralBlatt

Referenced by:

§28.26(ii).

Encodings:

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Reduction and evaluation of elliptic integrals. Math. Comp. 20 (94), pp. 223–231.

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External Links:

FullText, MathReview (I. A. Stegun), ZentralBlatt

Referenced by:

§19.37(iv).

Encodings:

BibTeX

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The resurgence properties of the large order asymptotics of the Anger-Weber function I. J. Class. Anal. 4 (1), pp. 1–39.

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External Links:

ISSN 1848-5979, Document, Link, MathReview (José Luis López), ZentralBlatt

Referenced by:

(11.11.10), (11.11.8), §11.11(iii).

Encodings:

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The resurgence properties of the large order asymptotics of the Anger-Weber function II. J. Class. Anal. 4 (2), pp. 121–147.

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External Links:

ISSN 1848-5979, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

(11.11.10), (11.11.8), §11.11(iii).

Encodings:

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A table of integrals of the error functions. J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.

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Notes:

See for additions and corrections same journal, Sect. B 75, 149–163 (1975)

External Links:

MathReview, ZentralBlatt

Referenced by:

§7.14(iii), §7.21, §7.7(iii).

Encodings:

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15: 11.13 Methods of Computation

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§11.13(i) Introduction

… ►The treatment of Lommel and Anger–Weber functions is similar. … ►

§11.13(iv) Differential Equations

►A comprehensive approach is to integrate the defining inhomogeneous differential equations (11.2.7) and (11.2.9) numerically, using methods described in §3.7. … ►

§11.13(v) Difference Equations

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16: 10.12 Generating Function and Associated Series

… ►Jacobi–Anger expansions: for $z,\theta \in ℂ$, …

17: 11.1 Special Notation

§11.1 Special Notation

… ►For the functions $J_{\nu }\left(z\right)$, $Y_{\nu }\left(z\right)$, $H_{\nu }^{(1)}\left(z\right)$, $H_{\nu }^{(2)}\left(z\right)$, $I_{\nu }\left(z\right)$, and $K_{\nu }\left(z\right)$ see §§10.2(ii), 10.25(ii). ►The functions treated in this chapter are the Struve functions ${𝐇}_{\nu }\left(z\right)$ and ${𝐊}_{\nu }\left(z\right)$, the modified Struve functions ${𝐋}_{\nu }\left(z\right)$ and ${𝐌}_{\nu }\left(z\right)$, the Lommel functions $s_{\mu ,\nu }\left(z\right)$ and $S_{\mu ,\nu }\left(z\right)$, the Anger function ${𝐉}_{\nu }\left(z\right)$, the Weber function ${𝐄}_{\nu }\left(z\right)$, and the associated Anger–Weber function ${𝐀}_{\nu }\left(z\right)$.

18: 11.16 Software

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§11.16(v) Anger and Weber Functions

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§11.16(vi) Integrals of Anger and Weber Functions

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19: 28 Mathieu Functions and Hill’s Equation

Chapter 28 Mathieu Functions and Hill’s Equation

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20: Bibliography B

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Pionic atoms. Annual Review of Nuclear and Particle Science 20, pp. 467–508.

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External Links:

Document

Referenced by:

§33.22(iv).

Encodings:

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Coulomb functions (negative energies). Comput. Phys. Comm. 20 (3), pp. 447–458.

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Notes:

Double-precision Fortran code.

External Links:

Document, Code

Referenced by:

1st item, 4th item.

Encodings:

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Tables of the Anger and Lommel-Weber Functions. Technical report Technical Report 53 and AFCRL 796, University Washington Press, Seattle.

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Notes:

Reviewed in Math. Comp., v. 17 (1963), pp.315–317.

Referenced by:

1st item.

Encodings:

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Some solutions of the problem of forced convection. Philos. Mag. Series 7 20, pp. 322–343.

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External Links:

Document, ZentralBlatt

Referenced by:

§10.73(iv).

Encodings:

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Bessel functions and modular relations of higher type and hyperbolic differential equations. Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (Tome Supplementaire), pp. 12–20.

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External Links:

MathReview (S. C. van Veen), ZentralBlatt

Referenced by:

§35.5(i).

Encodings:

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