Algorithm 855: Subroutines for the computation of Mathieu characteristic numbers and their general orders

ABSTRACT

A continued fraction function algorithm is developed to evaluate general-order Mathieu characteristic numbers, and a new technique is presented for evaluating the Mathieu determinant which can be used to compute the order directly. Approximate expressions are developed to estimate the orders and Mathieu characteristic numbers for the root, finding algorithms. The algorithms, with minor modifications, were used for computing Mathieu coefficients of general order. The algorithms can deal with a large range of Mathieu characteristic number c, real and complex order ν, and parameter h.

REFERENCES

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.0 General

General Terms:
Algorithms

Keywords:
Hill's determinant, Mathieu characteristic determinant, Mathieu characteristic numbers, Mathieu coefficients, Mathieu determinant, Mathieu differential equation, Mathieu functions, elliptic coordinates, general-order Mathieu functions, wave equation