Algorithms for the computation of all Mathieu functions of integer orders

ABSTRACT

The article presents methods for the computation of all Mathieu functions of integer order, which cover a large range of n and h; previous algorithms were limited to small values of n. The algorithms are given in sufficient detail to enable straightforward implementation. The algorithms can handle a large range of the order n (0-200) and the parameter h (0-4n).

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INDEX TERMS

Primary Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: C++

Additional Classification:
  G. Mathematics of Computing

General Terms:
Algorithms

Keywords:
Hill's determinant, Mathieu characteristic determinant, Mathieu characteristic numbers, Mathieu coefficients, Mathieu differential equation, Mathieu functions, elliptic cordinates, wave equation