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Anger–Weber functions

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1: 11.10 Anger–Weber Functions
§11.10 AngerWeber Functions
See accompanying text
Figure 11.10.1: Anger function J ν ( x ) for - 8 x 8 and ν = 0 , 1 2 , 1 , 3 2 . Magnify
See accompanying text
Figure 11.10.2: Weber function E ν ( x ) for - 8 x 8 and ν = 0 , 1 2 , 1 , 3 2 . Magnify
See accompanying text
Figure 11.10.3: Anger function J ν ( x ) for - 10 x 10 and 0 ν 5 . Magnify 3D Help
See accompanying text
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 ν ( z ) , Y ν ( z ) , H ν ( 1 ) ( z ) , H ν ( 2 ) ( z ) , I ν ( z ) , and K ν ( z ) see §§10.2(ii), 10.25(ii). The functions treated in this chapter are the Struve functions H ν ( z ) and K ν ( z ) , the modified Struve functions L ν ( z ) and M ν ( z ) , the Lommel functions s μ , ν ( z ) and S μ , ν ( z ) , the Anger function J ν ( z ) , the Weber function E ν ( z ) , and the associated AngerWeber function A ν ( z ) .
3: 11.14 Tables
§11.14(iv) AngerWeber Functions
§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 H n ( x , α ) for n = 0 , 1 , x = 0 ( .2 ) 10 , and α = 0 ( .2 ) 1.4 , 1 2 π , together with surface plots.

  • 4: 11.11 Asymptotic Expansions of Anger–Weber Functions
    §11.11 Asymptotic Expansions of AngerWeber Functions
    §11.11(i) Large | z | , Fixed ν
    §11.11(ii) Large | ν | , Fixed z
    11.11.17 A - ν ( ν + a ν 1 / 3 ) = 2 1 / 3 ν - 1 / 3 Hi ( - 2 1 / 3 a ) + O ( ν - 1 ) ,
    5: 11.13 Methods of Computation
    §11.13(i) Introduction
    The treatment of Lommel and AngerWeber functions is similar. …
    6: 11.16 Software
    §11.16(v) Anger and Weber Functions
    §11.16(vi) Integrals of Anger and Weber Functions
    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.
  • 8: 3.6 Linear Difference Equations
    Example 2. Weber Function
    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) J ν ( z ) , E ν ( z ) , A ν ( z ) 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. …