# Algorithm 352: characteristic values and associated solutions of Mathieu's differential equation [S22]

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### Cites background from "Algorithm 352: characteristic value..."

...Clemm published several pioneering Fortran routines to evaluate the Mathieu functions and their derivatives [17]....

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### Cites methods from "Algorithm 352: characteristic value..."

...The first integer order algorithm was that of Clemm [7]....

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...Leeb [18], Clemm [7], the Numerical Analysis Group at Delft [34], Dolbeeva [11], Toyama and Shogen [36], Arscott [2], Canosa [6], and Ikebe [16], and Sui and Ding [3’1] have all presented algorithms for integer order....

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...Recurrences of the form used by Clemm will converge to one eigenvalue in some regions of q and another eigenvalue in other regions of q....

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...The first integer order algorithm was that of Clemm [7]....

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...The eigenvalues and corresponding solutions to (1.1) with period ir or 2 n are infinite in number and can be ordered by the magnitude of a and whether the solution is even (a., n = 0,1,2 ,... )orodd(b~, n==l,2,3,... ), where n is the order [5] and indicates how many zeros the solution has for O x rr. Leeb [18], Clemm [7], the Numerical Analysis Group at Delft [34], Dolbeeva [11], Toyama and Shogen [36], Arscott [2], Canosa [6], and Ikebe [16], and Sui and Ding [3 1] have all presented algorithms for integer order....

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### Cites methods from "Algorithm 352: characteristic value..."

...The normalization factors adopted by Ince [6] are used, and Mathieu functions are computed using the algorithms in [7]....

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##### References

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