About the Project
NIST

Weber function

AdvancedHelp

(0.003 seconds)

1—10 of 68 matching pages

1: 11.10 Anger–Weber Functions
§11.10 Anger–Weber 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 Anger–Weber function A ν ( z ) .
3: 11.14 Tables
§11.14(iv) Anger–Weber 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: 11.13 Methods of Computation
    §11.13(i) Introduction
    The treatment of Lommel and Anger–Weber functions is similar. … See §3.6 for implementation of these methods, and with the Weber function E n ( x ) as an example.
    5: 11.16 Software
    §11.16(v) Anger and Weber Functions
    §11.16(vi) Integrals of Anger and Weber Functions
    6: 11.11 Asymptotic Expansions of Anger–Weber Functions
    §11.11 Asymptotic Expansions of Anger–Weber 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 ) ,
    7: 12.1 Special Notation
    Unless otherwise noted, primes indicate derivatives with respect to the variable, and fractional powers take their principal values. The main functions treated in this chapter are the parabolic cylinder functions (PCFs), also known as Weber parabolic cylinder functions: U ( a , z ) , V ( a , z ) , U ¯ ( a , z ) , and W ( a , z ) . …
    8: 3.6 Linear Difference Equations
    Example 2. Weber Function
    The Weber function E n ( 1 ) satisfies …
    3.6.15 E 2 n ( 1 ) 2 ( 4 n 2 - 1 ) π ,
    3.6.16 E 2 n + 1 ( 1 ) 2 ( 2 n + 1 ) π ;
    Table 3.6.1: Weber function w n = E n ( 1 ) computed by Olver’s algorithm.
    n p n e n e n / ( p n p n + 1 ) w n
    9: 10.58 Zeros
    §10.58 Zeros
    b n , m = y n + 1 2 , m ,
    y n ( b n , m ) = π 2 y n + 1 2 , m Y n + 1 2 ( y n + 1 2 , m ) .
    10: 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.