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)
35 Stirling Highway
Crawley WA 6009                      mailto:paul at physics.uwa.edu.au
AUSTRALIA                            http://physics.uwa.edu.au/~paul

```

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