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MathGroup Archive 2005

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Re: Computing Complex Series Solution using Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54684] Re: Computing Complex Series Solution using Mathematica
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Sun, 27 Feb 2005 01:29:08 -0500 (EST)
  • Organization: The University of Western Australia
  • References: <cvhiv9$s5r$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <cvhiv9$s5r$1 at smc.vnet.net>, Pratik Desai <pdesai1 at umbc.edu> 
wrote:

> Hello All,
> 
> I am trying to check the convergence or lack there of a complex series
> 
> Sinh[lamda*x]
> 
> where the first six lamda are given as
> lamda={-0.331+3.162*I,-0.435+6.234*I,-0.093+9.418*I,-0.203+12.566*I,-0.365+15.
> 669*I};
> x=Range[0,1,0.1];
> 
> I want to do more efficiently the following:
> 
> s4=Sinh[lamda[[1]]*x]+Sinh[lamda[[2]]*x]+Sinh[lamda[[3]]*x]+Sinh[lamda[[4]]*x]

Use Map and Total:

  lamda={-0.331+3.162*I,-0.435+6.234*I,-0.093+9.418*I,
          -0.203+12.566*I,-0.365+15.669*I};

  x=Range[0,1,0.1];

 Total[Sinh[# x] & /@ lamda]

You have 5 values in lamda. Do you really want to omit the last value as 
you have done in computing s4? If so then use

 Total[Sinh[# x] & /@ Most[lamda]]

I also note that the imaginary part of lamda is quite close to n Pi and 
that Sinh[x + I n Pi] simplfies.

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 6488 2734
School of Physics, M013                         Fax: +61 8 6488 1014
The University of Western Australia      (CRICOS Provider No 00126G)         
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Crawley WA 6009                      mailto:paul at physics.uwa.edu.au 
AUSTRALIA                            http://physics.uwa.edu.au/~paul


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