About the Project
NIST

Struve functions and modified Struve functions

AdvancedHelp

(0.005 seconds)

1—10 of 18 matching pages

1: 11.2 Definitions
§11.2 Definitions
§11.2(i) Power-Series Expansions
11.2.2 L ν ( z ) = - i e - 1 2 π i ν H ν ( i z ) = ( 1 2 z ) ν + 1 n = 0 ( 1 2 z ) 2 n Γ ( n + 3 2 ) Γ ( n + ν + 3 2 ) .
11.2.6 M ν ( z ) = L ν ( z ) - I ν ( z ) .
2: 11.12 Physical Applications
§11.12 Physical Applications
3: 11.8 Analogs to Kelvin Functions
§11.8 Analogs to Kelvin Functions
4: 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 ) .
5: 11.3 Graphics
See accompanying text
Figure 11.3.1: H ν ( x ) for 0 x 12 and ν = 0 , 1 2 , 1 , 3 2 , 2 , 3 . Magnify
See accompanying text
Figure 11.3.2: K ν ( x ) for 0 < x 16 and ν = 0 , 1 2 , 1 , 3 2 , 2 , 3 . Magnify
See accompanying text
Figure 11.3.3: H ν ( x ) for 0 x 12 and ν = - 3 , - 2 , - 3 2 , - 1 , - 1 2 . Magnify
See accompanying text
Figure 11.3.4: K ν ( x ) for 0 < x 16 and ν = - 4 , - 3 , - 2 , - 1 , 0 . … Magnify
See accompanying text
Figure 11.3.5: H ν ( x ) for 0 x 8 and - 4 ν 4 . Magnify 3D Help
6: 11.7 Integrals and Sums
§11.7(i) Indefinite Integrals
§11.7(ii) Definite Integrals
§11.7(iii) Laplace Transforms
§11.7(v) Compendia
7: 11.14 Tables
§11.14(ii) Struve Functions
§11.14(iii) Integrals
§11.14(v) Incomplete Functions
8: 11.4 Basic Properties
§11.4(i) Half-Integer Orders
§11.4(ii) Inequalities
§11.4(iii) Analytic Continuation
§11.4(v) Recurrence Relations and Derivatives
§11.4(vii) Zeros
9: 11.15 Approximations
§11.15(i) Expansions in Chebyshev Series
10: 11.5 Integral Representations
§11.5(i) Integrals Along the Real Line
11.5.4 M ν ( z ) = - 2 ( 1 2 z ) ν π Γ ( ν + 1 2 ) 0 1 e - z t ( 1 - t 2 ) ν - 1 2 d t , ν > - 1 2 ,
§11.5(ii) Contour Integrals
Mellin–Barnes Integrals
§11.5(iii) Compendia