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! MTU12 computes modified Mathieu functions of the first and second kind.
Discussion:
This procedure computes modified Mathieu functions of the first and
second kinds, Mcm(1)(2)(x,q) and Msm(1)(2)(x,q),
and their derivatives.
Licensing:
This routine is copyrighted by Shanjie Zhang and Jianming Jin. However,
they give permission to incorporate this routine into a user program
provided that the copyright is acknowledged.
Modified:
31 July 2012
Author:
Shanjie Zhang, Jianming Jin
Reference:
Shanjie Zhang, Jianming Jin,
Computation of Special Functions,
Wiley, 1996,
ISBN: 0-471-11963-6,
LC: QA351.C45.
Parameters:
Input, integer ( kind = 4 ) KF, the function code.
1 for computing Mcm(x,q);
2 for computing Msm(x,q).
Input, integer ( kind = 4 ) KC, the function code.
1, for computing the first kind
2, for computing the second kind or Msm(2)(x,q) and Msm(2)'(x,q)
3, for computing both the first and second kinds.
Input, integer ( kind = 4 ) M, the order of the Mathieu functions.
Input, real ( kind = 8 ) Q, the parameter of the Mathieu functions.
Input, real ( kind = 8 ) X, the argument of the Mathieu functions.
Output, real ( kind = 8 ) F1R, D1R, F2R, D2R, the values of
Mcm(1)(x,q) or Msm(1)(x,q), Derivative of Mcm(1)(x,q) or Msm(1)(x,q),
Mcm(2)(x,q) or Msm(2)(x,q), Derivative of Mcm(2)(x,q) or Msm(2)(x,q).
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| integer(kind=4) | :: | kf | ||||
| integer(kind=4) | :: | kc | ||||
| integer(kind=4) | :: | m | ||||
| real(kind=8) | :: | q | ||||
| real(kind=8) | :: | x | ||||
| real(kind=8) | :: | f1r | ||||
| real(kind=8) | :: | d1r | ||||
| real(kind=8) | :: | f2r | ||||
| real(kind=8) | :: | d2r |