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1: 28.12 Definitions and Basic Properties
§28.12 Definitions and Basic Properties
§28.12(ii) Eigenfunctions me ν ( z , q )
They have the following pseudoperiodic and orthogonality properties: …
2: 28.2 Definitions and Basic Properties
§28.2(ii) Basic Solutions w I , w II
§28.2(iv) Floquet Solutions
§28.2(vi) Eigenfunctions
3: 28.20 Definitions and Basic Properties
§28.20(ii) Solutions Ce ν , Se ν , Me ν , Fe n , Ge n
§28.20(iii) Solutions M ν ( j )
§28.20(iv) Radial Mathieu Functions Mc n ( j ) , Ms n ( j )
§28.20(vi) Wronskians
§28.20(vii) Shift of Variable
4: 28.27 Addition Theorems
§28.27 Addition Theorems
Addition theorems provide important connections between Mathieu functions with different parameters and in different coordinate systems. …
5: 28.33 Physical Applications
§28.33 Physical Applications
Mathieu functions occur in practical applications in two main categories: …
§28.33(ii) Boundary-Value Problems
§28.33(iii) Stability and Initial-Value Problems
  • Torres-Vega et al. (1998) for Mathieu functions in phase space.

  • 6: Gerhard Wolf
    Wolf has published papers on Mathieu functions, orthogonal polynomials, and Heun functions. His book Mathieu Functions and Spheroidal Functions and Their Mathematical Foundations: Further Studies (with J. …
  • 7: 28 Mathieu Functions and Hill’s Equation
    Chapter 28 Mathieu Functions and Hill’s Equation
    8: 28.22 Connection Formulas
    §28.22 Connection Formulas
    The joining factors in the above formulas are given by …
    ge m ( 0 , h 2 ) = 1 2 π S m ( h 2 ) ( g o , m ( h ) ) 2 se m ( 0 , h 2 ) .
    28.22.13 M ν ( 1 ) ( z , h ) = M ν ( 1 ) ( 0 , h ) me ν ( 0 , h 2 ) Me ν ( z , h 2 ) .
    9: 28.11 Expansions in Series of Mathieu Functions
    §28.11 Expansions in Series of Mathieu Functions
    28.11.1 f ( z ) = α 0 ce 0 ( z , q ) + n = 1 ( α n ce n ( z , q ) + β n se n ( z , q ) ) ,
    28.11.3 1 = 2 n = 0 A 0 2 n ( q ) ce 2 n ( z , q ) ,
    28.11.4 cos 2 m z = n = 0 A 2 m 2 n ( q ) ce 2 n ( z , q ) , m 0 ,
    28.11.7 sin ( 2 m + 2 ) z = n = 0 B 2 m + 2 2 n + 2 ( q ) se 2 n + 2 ( z , q ) .
    10: 28.21 Graphics
    §28.21 Graphics
    Radial Mathieu Functions: Surfaces
    See accompanying text
    Figure 28.21.6: Ms 1 ( 2 ) ( x , h ) for 0.2 h 2 , 0 x 2 . Magnify 3D Help