Fayez A. Alhargan

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.

Article

Fayez A. Alhargan.
" Algorithm 855: Subroutines for the computation of Mathieu characteristic numbers and their general orders."
*ACM Transactions on Mathematical Software*.
doi:10.1145/1163641.1163646.
Retrieved 02/26/2021 from researchcompendia.org/compendia/2013.294/

**Compendium Type**: Published Papers

**Primary Research Field**: Computer and Information Sciences

**Secondary Research Field**: Mathematics

**Content License**: Public Domain Mark

**Code License**: MIT License

created 12/12/2013

modified 01/16/2014

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