# Anger–Weber functions

(0.004 seconds)

## 1—10 of 11 matching pages

##### 1: 11.10 Anger–Weber Functions
###### §11.10 Anger–WeberFunctions Figure 11.10.1: Anger function 𝐉 ν ⁡ ( x ) for − 8 ≤ x ≤ 8 and ν = 0 , 1 2 , 1 , 3 2 . Magnify Figure 11.10.2: Weber function 𝐄 ν ⁡ ( x ) for − 8 ≤ x ≤ 8 and ν = 0 , 1 2 , 1 , 3 2 . Magnify Figure 11.10.3: Anger function 𝐉 ν ⁡ ( x ) for − 10 ≤ x ≤ 10 and 0 ≤ ν ≤ 5 . Magnify 3D Help Figure 11.10.4: Weber function 𝐄 ν ⁡ ( x ) for − 10 ≤ x ≤ 10 and 0 ≤ ν ≤ 5 . Magnify 3D Help
##### 2: 11.1 Special Notation
###### §11.1 Special Notation
For the functions $J_{\nu}\left(z\right)$, $Y_{\nu}\left(z\right)$, ${H^{(1)}_{\nu}}\left(z\right)$, ${H^{(2)}_{\nu}}\left(z\right)$, $I_{\nu}\left(z\right)$, and $K_{\nu}\left(z\right)$ see §§10.2(ii), 10.25(ii). The functions treated in this chapter are the Struve functions $\mathbf{H}_{\nu}\left(z\right)$ and $\mathbf{K}_{\nu}\left(z\right)$, the modified Struve functions $\mathbf{L}_{\nu}\left(z\right)$ and $\mathbf{M}_{\nu}\left(z\right)$, the Lommel functions $s_{{\mu},{\nu}}\left(z\right)$ and $S_{{\mu},{\nu}}\left(z\right)$, the Anger function $\mathbf{J}_{\nu}\left(z\right)$, the Weber function $\mathbf{E}_{\nu}\left(z\right)$, and the associated AngerWeber function $\mathbf{A}_{\nu}\left(z\right)$.
##### 3: 11.14 Tables
###### §11.14(v) Incomplete Functions
• Agrest and Maksimov (1971, Chapter 11) defines incomplete Struve, Anger, and Weber functions and includes tables of an incomplete Struve function $\mathbf{H}_{n}\left(x,\alpha\right)$ for $n=0,1$, $x=0(.2)10$, and $\alpha=0(.2)1.4,\tfrac{1}{2}\pi$, together with surface plots.

##### 5: 11.13 Methods of Computation
###### §11.13(i) Introduction
The treatment of Lommel and AngerWeber functions is similar. …
##### 7: Bibliography N
• G. Nemes (2014b) The resurgence properties of the large order asymptotics of the Anger-Weber function I. J. Class. Anal. 4 (1), pp. 1–39.
• G. Nemes (2014c) The resurgence properties of the large order asymptotics of the Anger-Weber function II. J. Class. Anal. 4 (2), pp. 121–147.
##### 9: Bibliography B
• G. D. Bernard and A. Ishimaru (1962) Tables of the Anger and Lommel-Weber Functions. Technical report Technical Report 53 and AFCRL 796, University Washington Press, Seattle.
• ##### 10: Software Index
 Open Source With Book Commercial … 11.16(v) $\mathbf{J}_{\nu}\left(z\right)$, $\mathbf{E}_{\nu}\left(z\right)$, $\mathbf{A}_{\nu}\left(z\right)$ a ✓ ✓ ✓ ✓ a …
‘✓’ indicates that a software package implements the functions in a section; ‘a’ indicates available functionality through optional or add-on packages; an empty space indicates no known support. … In the list below we identify four main sources of software for computing special functions. …
• Commercial Software.

Such software ranges from a collection of reusable software parts (e.g., a library) to fully functional interactive computing environments with an associated computing language. Such software is usually professionally developed, tested, and maintained to high standards. It is available for purchase, often with accompanying updates and consulting support.

• The following are web-based software repositories with significant holdings in the area of special functions. …