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Struve functions

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1: 11.12 Physical Applications
§11.12 Physical Applications
Applications of Struve functions occur in water-wave and surface-wave problems (Hirata (1975) and Ahmadi and Widnall (1985)), unsteady aerodynamics (Shaw (1985) and Wehausen and Laitone (1960)), distribution of fluid pressure over a vibrating disk (McLachlan (1934)), resistive MHD instability theory (Paris and Sy (1983)), and optical diffraction (Levine and Schwinger (1948)). More recently Struve functions have appeared in many particle quantum dynamical studies of spin decoherence (Shao and Hänggi (1998)) and nanotubes (Pedersen (2003)).
2: 11.8 Analogs to Kelvin Functions
§11.8 Analogs to Kelvin Functions
For properties of Struve functions of argument x e ± 3 π i / 4 see McLachlan and Meyers (1936).
3: 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 ) .
4: 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
5: 11.7 Integrals and Sums
§11.7(i) Indefinite Integrals
§11.7(ii) Definite Integrals
§11.7(iii) Laplace Transforms
§11.7(v) Compendia
6: 11.14 Tables
§11.14(ii) Struve Functions
§11.14(iii) Integrals
§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.

  • 7: 11.2 Definitions
    §11.2 Definitions
    §11.2(i) Power-Series Expansions
    Particular solutions: … Particular solutions: …
    8: 11.4 Basic Properties
    §11.4(i) Half-Integer Orders
    §11.4(ii) Inequalities
    §11.4(iv) Expansions in Series of Bessel Functions
    §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(ii) Contour Integrals
    Mellin–Barnes Integrals
    11.5.8 ( 1 2 x ) - ν - 1 H ν ( x ) = - 1 2 π i - i i π csc ( π s ) Γ ( 3 2 + s ) Γ ( 3 2 + ν + s ) ( 1 4 x 2 ) s d s , x > 0 , ν > - 1 ,
    §11.5(iii) Compendia