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Thread Subject:
need complex roots

Subject: need complex roots

From: Ramesh Kudenatti

Date: 8 Jan, 2009 17:17:02

Message: 1 of 3

Hi
Could anyone tell me how to find the roots of equation involving the transcendental functions like Airy function and its derivative with complex argument? My function is given below.
AiryAiPrime(Z)-c1 Exp[I Pi/6] ==0 where Z = I W (6 I k)^(-2/3), W is unknown, c1 and k are known.

Requesting..........

Subject: need complex roots

From: Roger Stafford

Date: 8 Jan, 2009 17:48:01

Message: 2 of 3

"Ramesh Kudenatti" <ramesh@bub.ernet.in> wrote in message <gk5cee$bt5$1@fred.mathworks.com>...
> Hi
> Could anyone tell me how to find the roots of equation involving the transcendental functions like Airy function and its derivative with complex argument? My function is given below.
> AiryAiPrime(Z)-c1 Exp[I Pi/6] ==0 where Z = I W (6 I k)^(-2/3), W is unknown, c1 and k are known.
>
> Requesting..........

  For using 'fsolve' to find complex roots see the recent discussion of this problem at:

"finding complex root from nonlinear equations"
http://www.mathworks.com/matlabcentral/newsreader/view_thread/241861

Roger Stafford

Subject: need complex roots

From: Roger Stafford

Date: 8 Jan, 2009 18:13:02

Message: 3 of 3

"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in message <gk5e8h$cgs$1@fred.mathworks.com>...
> "Ramesh Kudenatti" <ramesh@bub.ernet.in> wrote in message <gk5cee$bt5$1@fred.mathworks.com>...
> > Hi
> > Could anyone tell me how to find the roots of equation involving the transcendental functions like Airy function and its derivative with complex argument? My function is given below.
> > AiryAiPrime(Z)-c1 Exp[I Pi/6] ==0 where Z = I W (6 I k)^(-2/3), W is unknown, c1 and k are known.
> >
> > Requesting..........
>
> For using 'fsolve' to find complex roots see the recent discussion of this problem at:
>
> "finding complex root from nonlinear equations"
> http://www.mathworks.com/matlabcentral/newsreader/view_thread/241861
>
> Roger Stafford

  My apologies! I hadn't noticed until now that you participated in that thread yourself, Ramesh.

  The only additional thing I can think of suggesting is that you first find the complex roots Z in AiryAiPrime(Z) = c1*exp{pi/6*i) using 'fsolve'. After that you can solve Z = i*W*(6*k*i)^(-2/3) for W by

 W = Z*(6*k)^(2/3)*i^(-1/3)

which has three trivially easy roots for each Z root found. This will perhaps make things easier for using 'fsolve' by reducing the number of roots for it to find.

Roger Stafford

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