(For other notation see Notation for the Special Functions.)
|order of the Mathieu function or modified Mathieu function. (When is an integer it is often replaced by .)|
|arbitrary small positive number.|
|real or complex parameters of Mathieu’s equation with .|
|primes||unless indicated otherwise, derivatives with respect to the argument|
The main functions treated in this chapter are the Mathieu functions
and the modified Mathieu functions
The functions and are also known as the radial Mathieu functions.
The eigenvalues of Mathieu’s equation are denoted by
The notation for the joining factors is
Alternative notations for the parameters and are shown in Table 28.1.1.
|Erdélyi et al. (1955)|
|Meixner and Schäfke (1954)|
|Moon and Spencer (1971)|
|Whittaker and Watson (1927)|
Alternative notations for the functions are as follows.
Arscott (1964b) also uses for .
The radial functions and are denoted by and , respectively.