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Re: bad Mathieu functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg108296] Re: [mg108226] bad Mathieu functions
  • From: "David Park" <djmpark at comcast.net>
  • Date: Sat, 13 Mar 2010 07:54:38 -0500 (EST)
  • References: <22468552.1268308558188.JavaMail.root@n11>

Use greater WorkingPrecision.

Plot[I ce1[3, q, I], {q, 0, 100},
 WorkingPrecision -> 30,
 PlotRange -> {-1, 1} 5] 


David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/  



From: becko BECKO [mailto:becko565 at hotmail.com] 


I am no expert in Mathieu functions, but I don't think this gives the right
result:

ce1[r_, q_, z_] := MathieuCPrime[MathieuCharacteristicA[r, q], q, z]

Plot[I ce1[3, q, I], {q, 0, 1000}]


In another system you get a smooth graph, making very small oscillations
about zer o as q increases. I've read that Mathieu functions are difficult
to deal with. I guess that Mathematica's implementation doesn't support
arbitrary values of the parameters. I made a bug report in the WRI site.
Maybe someone here has some comments to share? It would be nice if there
were a package or something with more robust implementations of Mathieu
functions.
 		 	   		 



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